51013180 the Derivatives Market Overview

THE SOUTH AFRICAN INSTITUTE OF FINANCIAL MARKETS

THE DERIVATIVES MARKET

© Quoin Institute (Pty) Limited (2010)

AP Faure

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IMPORTANT INFORMATION

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average learner should go through the material at least 3 times and do the self-test questions before

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THE DERIVATIVE MARKET

TABLE OF CONTENTS

CHAPTER 1: THE DERIVATIVE MARKETS IN CONTEXT ........................................................ 7

1.1 CHAPTER ORIENTATION ................................................................................................................................... 7

1.2 LEARNING OUTCOMES OF THIS CHAPTER ........................................................................................................ 7

1.3 INTRODUCTION ................................................................................................................................................ 7

1.4 THE FINANCIAL SYSTEM IN BRIEF ..................................................................................................................... 8

1.5 ULTIMATE LENDERS AND BORROWERS ............................................................................................................ 8

1.6 FINANCIAL INTERMEDIARIES ........................................................................................................................... 10

1.7 FINANCIAL INSTRUMENTS ............................................................................................................................... 10

1.8 SPOT FINANCIAL MARKETS ............................................................................................................................. 12

1.9 INTEREST RATES .............................................................................................................................................. 15

1.10 THE DERIVATIVE MARKETS.............................................................................................................................. 15

1.11 REVIEW QUESTIONS AND ANSWERS ............................................................................................................... 19

CHAPTER 2: FORWARDS ................................................................................................. 20

2.1 CHAPTER ORIENTATION .................................................................................................................................. 20

2.2 LEARNING OUTCOMES OF THIS CHAPTER ....................................................................................................... 20

2.3 INTRODUCTION ............................................................................................................................................... 20

2.4 SPOT MARKET ................................................................................................................................................. 21

2.5 INTRODUCTION TO FORWARD MARKETS ........................................................................................................ 21

2.6 A SIMPLE EXAMPLE ......................................................................................................................................... 23

2.7 FORWARD MARKETS ....................................................................................................................................... 25

2.8 FORWARDS IN THE DEBT MARKETS ................................................................................................................ 26

2.9 FORWARDS IN THE EQUITY MARKET ............................................................................................................... 40

2.10 FORWARDS IN THE FOREIGN EXCHANGE MARKET .......................................................................................... 41

2.11 FORWARDS IN THE COMMODITIES MARKET ................................................................................................... 49

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2.12 FORWARDS ON DERIVATIVES .......................................................................................................................... 50

2.13 ORGANISATIONAL STRUCTURE OF FORWARD MARKETS ................................................................................ 51

2.14 REVIEW QUESTIONS AND ANSWERS ............................................................................................................... 53

2.15 USEFUL ACTIVITIES .......................................................................................................................................... 56

CHAPTER 3: FUTURES ..................................................................................................... 57

3.1 CHAPTER ORIENTATION .................................................................................................................................. 57

3.2 LEARNING OUTCOMES OF THIS CHAPTER ....................................................................................................... 57

3.3 INTRODUCTION ............................................................................................................................................... 57

3.4 FUTURES DEFINED ........................................................................................................................................... 58

3.5 AN EXAMPLE ................................................................................................................................................... 61

3.6 FUTURES TRADING PRICE VERSUS SPOT PRICE ................................................................................................ 64

3.7 TYPES OF FUTURES CONTRACTS ...................................................................................................................... 67

3.8 ORGANISATIONAL STRUCTURE OF FUTURES MARKETS ................................................................................... 68

3.9 CLEARING HOUSE ............................................................................................................................................ 70

3.10 MARGINING AND MARKING TO MARKET ........................................................................................................ 70

3.11 OPEN INTEREST ............................................................................................................................................... 71

3.12 CASH SETTLEMENT VERSUS PHYSICAL SETTLEMENT ........................................................................................ 72

3.13 PAYOFF WITH FUTURES (RISK PROFILE)........................................................................................................... 72

3.14 PRICING OF FUTURES (FAIR VALUE VERSUS TRADING PRICE) .......................................................................... 73

3.15 FAIR VALUE PRICING OF SPECIFIC FUTURES..................................................................................................... 76

3.16 BASIS AND NET CARRY COST ........................................................................................................................... 84

3.17 PARTICIPANTS IN THE FUTURES MARKET ........................................................................................................ 85

3.18 HEDGING WITH FUTURES ............................................................................................................................ 89

3.19 SOUTH AFRICAN FUTURES MARKET CONTRACTS ............................................................................................ 94

3.20 RISK MANAGEMENT BY SAFEX ........................................................................................................................ 95

3.21 MECHANICS OF DEALING IN FUTURES ............................................................................................................. 96

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3.22 SIZE OF FUTURES MARKET IN SOUTH AFRICA .................................................................................................. 99

3.23 ECONOMIC SIGNIFICANCE OF FUTURES MARKETS ........................................................................................ 100

3.24 REVIEW QUESTIONS AND ANSWERS ............................................................................................................. 103

3.25 USEFUL ACTIVITIES ........................................................................................................................................ 106

CHAPTER 4 : SWAPS ..................................................................................................... 107

4.1 CHAPTER ORIENTATION ................................................................................................................................ 107

4.2 LEARNING OUTCOMES OF THIS CHAPTER ..................................................................................................... 107

4.3 INTRODUCTION ............................................................................................................................................. 107

4.4 INTEREST RATE SWAPS.................................................................................................................................. 109

4.5 CURRENCY SWAPS ........................................................................................................................................ 115

4.6 EQUITY SWAPS ............................................................................................................................................. 119

4.7 COMMODITY SWAPS .................................................................................................................................... 121

4.8 LISTED SWAPS ............................................................................................................................................... 122

4.9 ORGANISATIONAL STRUCTURE OF SWAP MARKET ....................................................................................... 122



CHAPTER 5: OPTIONS ................................................................................................... 129



5.3 INTRODUCTION ............................................................................................................................................. 129

5.4 THE BASICS OF OPTIONS ............................................................................................................................... 131

5.5 INTRINSIC VALUE AND TIME VALUE .............................................................................................................. 137

5.6 OPTION VALUATION/PRICING ....................................................................................................................... 139

5.7 ORGANISATIONAL STRUCTURE OF OPTION MARKETS ................................................................................... 144

5.8 OPTIONS ON DERIVATIVES: FUTURES ............................................................................................................ 146

5.9 OPTIONS ON DERIVATIVES: SWAPS ............................................................................................................... 152

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5.10 OPTIONS ON DEBT MARKET INSTRUMENTS ................................................................................................. 154

5.11 OPTIONS ON EQUITY MARKET INSTRUMENTS .............................................................................................. 166

5.12 OPTIONS ON FOREIGN EXCHANGE ................................................................................................................ 170

5.13 OPTIONS ON COMMODITIES ......................................................................................................................... 171

5.14 OPTION STRATEGIES ..................................................................................................................................... 172

5.15 EXOTIC OPTIONS ........................................................................................................................................... 175



CHAPTER 6: OTHER DERIVATIVE INSTRUMENTS ............................................................ 181



6.3 INTRODUCTION ............................................................................................................................................. 181

6.4 SECURITISATION ........................................................................................................................................... 182

6.5 CREDIT DERIVATIVES ..................................................................................................................................... 184

6.6 WEATHER DERIVATIVES ................................................................................................................................ 187

6.7 SUMMARY OF DERIVATIVE INSTRUMENTS ................................................................................................... 191


CHAPTER 7: GLOSSARY OF TERMS ................................................................................ 195

CHAPTER 8: BIBLIOGRAPHY .......................................................................................... 199

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CHAPTER 1: THE DERIVATIVE MARKETS IN CONTEXT

NOTE FOR SAIFM RPE EXAM STUDENTS

ONLY THE SECTION ON “THE DERIVATIVE MARKETS” (PAGES 13 – 16) WILL BE EXAMINED

1.1 CHAPTER ORIENTATION

CHAPTERS OF THE DERIVATIVE MARKETS

Chapter 1 The derivative markets in context

Chapter 2 Forwards

Chapter 3 Futures

Chapter 4 Swaps

Chapter 5 Options

Chapter 6 Other derivative instruments

1.2 LEARNING OUTCOMES OF THIS CHAPTER

After studying this chapter the learner should:

• Understand the context and basics of the derivative markets

1.3 INTRODUCTION

The purpose of this chapter is to provide the context of the derivative markets. The context of the

derivatives markets is the financial system and its financial markets, and the commodities markets. This brief

chapter has the following sections:

• The financial system in brief

• Ultimate lenders and borrowers

• Financial intermediaries

• Financial instruments

• Spot financial markets

• Interest rates

• The derivative markets

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1.4 THE FINANCIAL SYSTEM IN BRIEF

The financial system is essentially concerned with borrowing and lending and may be depicted simply as in

Figure 1.1.

LENDERS

(surplus budget units)

HOUSEHOLD SECTOR

CORPORATE SECTOR

GOVERNMENT SECTOR

FOREIGN SECTOR

BORROWERS

(def icit budget units)

HOUSEHOLD SECTOR

CORPORATE SECTOR

GOVERNMENT SECTOR

FOREIGN SECTOR

Securities

FINANCIAL

INTERMEDIARIES

Securities

Indirect investment

Securities

Direct investment

Figure 1.1: simplified financial system

The financial system has six essential elements:

• First: ultimate lenders (surplus economic units) and borrowers (deficit economic units), i.e. the non-

financial economic units that undertake the lending and borrowing process.

• Second: financial intermediaries which intermediate the lending and borrowing process; they

interpose themselves between the lenders and borrowers.

• Third: financial instruments, which are created to satisfy the financial requirements of the various

participants; these instruments may be marketable (e.g. treasury bills) or non-marketable

(retirement annuity).

• Fourth: the creation of money when demanded; banks have the unique ability to create money.

• Fifth: financial markets, i.e. the institutional arrangements and conventions that exist for the issue

and trading (dealing) of the financial instruments;

• Sixth: price discovery, i.e. the price of equity and the price of money / debt (the rate of interest) are

“discovered” (made and determined) in the financial markets. Prices have an allocation of funds

function.

We touch upon five of the elements of the financial system below (i.e. excluding the creation of money),

because they serve as a useful introduction to the derivative markets.

1.5 ULTIMATE LENDERS AND BORROWERS

The ultimate lenders can be split into the four broad categories of the economy: the household sector, the

corporate (or business) sector, the government sector and the foreign sector. Exactly the same non-financial

economic units also appear on the other side of the financial system as ultimate borrowers. This is because

the members of the four categories may be either surplus or deficit units or both at the same time. An

example of the latter is government: the governments of most countries are permanent borrowers (usually

long-term), while at the same time having short-term funds in their accounts at the central bank and the

private banks, pending spending.

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TABLE 1.1: FINANCIAL INTERMEDIARIES IN SOUTH AFRICA

DEPOSIT INTERMEDIARIES

South African Reserve Bank (SARB)

Corporation for Public Deposits (CPD)

Land and Agricultural Bank (LAB)

Private sector banks

Postbank

NON-DEPOSIT INTERMEDIARIES

Contractual intermediaries (CIs)

Short-term insurers

Long-term insurers

Retirement funds (pension and provident funds)

Public Investment Commissioners (PIC)

COLLECTIVE INVESTMENT SCHEMES (CISs)

Securities unit trusts (SUTs)

Property unit trusts (PUTs)

Exchange traded funds (ETFs)

Participation mortgage bond schemes (PMBSs)

Alternative investments (AIs)

Hedge funds (HFs)

Private equity funds (PEFs)

QUASI-FINANCIAL INTERMEDIARIES (QFIs)

Development Finance Intermediaries (DFIs) (Land Bank, IDC, DBSA, etc)

Investment trusts / companies

Finance companies

Securitisation vehicles (SPVs)

Savings and credit cooperatives (SACCOs)

Friendly societies

Micro lenders

Buying associations

Stokvels

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1.6 FINANCIAL INTERMEDIARIES

Financial intermediaries exist because there is a conflict between lenders and borrowers in terms of their

financial requirements (term, risk, volume, etc). They solve this divergence of requirements and perform

many other functions such as lessening risk, creating a payments system, monetary policy, etc.

Financial intermediaries may be classified in many ways. A list of financial intermediaries in South Africa,

according to our categorisation preference, is as shown in Table 1.1.

The main financial intermediaries (or categories) and their relationship to one another may be depicted as in

Figure 1.2.

LENDERS

HOUSEHOLD SECTOR

CORPORATE SECTOR

GOVERNMENT SECTOR

FOREIGN SECTOR

BORROWERS

HOUSEHOLD SECTOR

CORPORATE SECTOR

GOVERNMENT SECTOR

FOREIGN SECTOR

INVESTMENT VEHICLES

CIs

CISs

AIs

CENTRAL BANK

BANKS

BANKS

Debt & shares

Debt & shares

Debt & shares

CDs

Certif icates of deposit (CDs)

Investment vehicle securities

QFIs:DFIs, SPVs, Finance co’s Investment co’s

DebtInterbankdebt

Figure 1.2: simplified relationship of financial intermediaries

Interbankdebt

Debt & shares

Debt & shares

Certif icates of deposit (CDs)

1.7 FINANCIAL INSTRUMENTS

As a result of the process of financial intermediation, and in order to satisfy the investment requirements of

the ultimate lenders and the financial intermediaries (in their capacity as borrowers and lenders), a wide

array of financial instruments exist. The instruments are either non-marketable (e.g. retirement annuities,

insurance policies), which means that their markets are only primary markets (see next section), or

marketable, which means that they are issued in their primary markets and traded in their secondary

markets (see next section). The marketable financial instruments (also called securities) that exist in the

South African financial markets (defined in the next section) are revealed in Table 1.21.

1 All the financial intermediaries are repeated in this table to indicate that many financial intermediaries do not issue securities

that are marketable.

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TABLE 1.2: MARKETABLE SECURITIES IN SOUTH AFRICA

Ultimate borrowers / financial intermediaries Instrument

ULTIMATE BORROWERS

HOUSEHOLD SECTOR

CORPORATE SECTOR

GOVERNMENT SECTOR

Central government

Provincial governments

Local governments

Public enterprises

FOREIGN SECTOR

FINANCIAL INTERMEDIARIES

DEPOSIT INTERMEDIARIES

South African Reserve Bank (SARB)

Corporation for Public Deposits (CPD)

Private sector banks

NON-DEPOSIT INTERMEDIARIES

Contractual intermediaries (CIs)

Short-term insurers

Long-term insurers

Retirement funds

Public Investment Commissioners (PIC)

Collective investment schemes (CISs)

Securities unit trusts (SUTs)

Property unit trusts (PUTs)

Exchange traded funds (ETFs)

Participation bond schemes (PBSs)

Alternative investments

Hedge funds (HFs)

Private equity funds (PEFs)

QUASI-FINANCIAL INTERMEDIARIES

Development Finance Institutions (DFIs)

Investment trusts / companies

Finance companies

Securitisation vehicles (SPVs)

Savings and credit cooperatives

Friendly societies

Micro lenders

Buying associations

Stokvels

-

Equity*, corporate bonds, BA, CP, PN

-

TB, RSA bonds

-

Local government bonds

Public enterprise bonds, CP

Foreign shares, bonds, CP

SARB debentures

-

NCDs

-

-

-

-

SUT units (marketable to issuer)

PUT units (JSE Listed)

ETF PI (marketable to issuer)

PBS PI (marketable to issuer)

HF PI (marketable to issuer)

PEF PI (marketable to issuer)

CP, bonds

-

CP, bonds

CP, bonds

-

-

-

-

-

* = ordinary and preference; BA = bank acceptance; PN = promissory note; CP = commercial paper; CDO = collateralised

debt obligation; MBS = mortgage backed security; PI = participation interest.

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1.8 SPOT FINANCIAL MARKETS

1.8.1 Primary and secondary markets

As noted, there exist primary and secondary markets. The former are the markets that exist for the issue of

new securities (marketable and non-marketable), while the latter are the markets that exist for the trading

of existing marketable securities. It should be evident that in the primary markets the issuers (borrowers)

receive money from the lenders (investors), while in the secondary markets the issuers do not; money flows

from the buyers to the sellers. This is depicted in Figure 1.3.

LENDERS BORROWERS

money

securities

BUYERS SELLERS

money

securities

the difference

the difference

Figure 1.3: primary and secondary markets

primary market

secondary market

The secondary financial markets evolved to satisfy the needs of lenders (investors) to buy and sell

(exchange) securities when the need arose. Some markets naturally exist in a safe (i.e. low risk)

environment, while for others a safe environment has been created. The former markets are called over-the-

counter (OTC) markets, and the latter the formalised (or exchange-driven) markets. The OTC markets are the

foreign exchange and money markets (partly exchange-driven), which essentially are the domain of the well-

capitalised banks, while the exchange-driven markets are the share (or equity) and bond markets. These

markets may be depicted as in Figure1.4.

Figure 1.4: financial markets

LOCALFINANCIAL

MARKETS

capital market

debt market/ interest-bearingmarket /

fixed-interestmarketMoney

market

Forexmarket

= conduit

Share market

Bond market

Forex market = conduit

FOREIGN FINANCIAL MARKETS

FOREIGN FINANCIAL MARKETS

ST debt market

LT debt market

Share market

These markets are also called the spot (or cash) financial markets, as opposed to the derivative markets.

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1.8.2 Debt market

Ignoring the share / equity market, the financial market, is a debt market, in that in this market debt

instruments are issued and exchanged. Interest is paid on debt instruments (hence the other name: interest-

bearing market), as opposed to dividends that are paid on shares / equities. The debt markets are also called

the fixed-interest markets, but this is a misnomer because interest may be floating, i.e. reset at intervals,

during the life of the instruments.

The debt market and it can be split into the short-term debt market and the long-term debt market. The

money market can be defined as the short-term marketable securities market or as the market for all short-

term debt, marketable and non-marketable. Some scholars also term the market as the market for

wholesale debt. Our preference is to define the money market as the market for all short-term debt – and

the reason is that in this market the volume of non-marketable debt far outstrips the volume of marketable

debt. Also the genesis of money market interest rates takes place in the non-marketable debt market

(specifically the interbank markets – there are three interbank “markets”, but we will not cover this detail

here).

The other part of the debt market is the long-term debt market, which is (obviously) the market for the issue

and trading of long-term debt instruments. The trading of long-term debt only applies to the marketable

securities of the long-term debt market, and this applies to bonds. Thus the bond market is the market for

the issue (primary market) and trading (secondary market) of marketable long-term securities.

The money and bond markets are differentiated according to term to maturity: the cut-off maturity is

arbitrarily set at one year. Thus, we define the money market as the market for the issue (marketable and

non-marketable) and trading (marketable) of securities with maturities of less than one year, and the bond

market as the issue and trading of marketable securities with maturities of longer than one year (called

bonds).

The definition of the bond market is acceptable but we need to take the money market a little further –

because it is much more than the issue and trading of securities of less than one year. It includes the all-

important call money market, i.e. the one-day non-marketable deposit market (which plays a major role in

interest rate discovery), and the interbank markets referred to earlier, which also covers significant

operations of the Reserve Bank in this market, the bond market and the foreign exchange market. It

operates in these markets in the form of open market operations in order to establish a certain desired

“money market shortage”, i.e. level of borrowed reserves, and this it provides via the interbank market.

These borrowed reserves are provided at the Bank’s accommodation rate, nowadays called the repo rate (in

the past called Bank rate). The genesis of interest rates is here (one of the interbank markets) which has a

major impact on another (the bank-to-bank interbank market) and then on bank call money rates ... and so

on.

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Thus, the money market encompasses the following markets (ignoring the money market derivative markets

for a moment):

• Markets in the short-term debt securities of ultimate borrowers.

• Markets in the short-term deposit securities of banks.

• Markets in the short-term deposit securities of the central bank (bank notes and coins and securities

issued for monetary policy purposes).

• Interbank market between private sector banks.

• Interbank markets between the central bank and the private sector banks.

1.8.3 Equity / share market

The equity market is the market for the issue and trading of equities. The term share (also called equity)

refers to permanent capital (ordinary shares) and long-term semi-permanent capital in the form of

preference shares. Ordinary shares are permanent capital in the sense that they represent a share in the

ownership of a company. Preference shares have preference over ordinary shares, and creditors (e.g.

holders of bonds) enjoy preference over preference shares in the event of the liquidation of the company.

1.8.4 Foreign exchange market

The foreign exchange (forex) market, strictly speaking, is not a financial market.2 However, since residents

(ignoring exchange controls for a moment) are able to borrow or lend offshore, and foreigners are able to

lend to or borrow from local institutions, the forex market (which allows these transactions to take place)

has a domestic and foreign lending or borrowing dimension, and can be viewed as being closely allied to the

domestic financial market.

When we focus on the ultimate lenders and borrowers in our depiction of the financial system shown

earlier, we observe that these sectors include the foreign sector. This is where the foreign exchange market

fits in. The foreign sector is able to supply funds to South Africa, domestic institutions are able to lend to the

foreign sector, and the foreign sector is able to borrow funds in the local market (i.e. issue securities in the

local market). The unbound forex markets of the world allow this to take place. As indicated above, the forex

market should be seen as a conduit for foreigners to the local financial and goods / services markets and for

locals to the foreign financial and goods / services markets.

It will be apparent that in order for a forex market to function there needs to be a demand for and a supply

of forex. Demand is the demand for, say, US dollars, the counterpart of which is the supply of rand. This

cannot be satisfied without a supply of forex (say US dollars), the counterpart of which is a demand for rand.

The forex market brings these demanders and suppliers together.

2 Because lending and borrowing domestically do not take place in this market.

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Figure 1.5: normal yield curve

rate% pa

term to maturity

2years

4years

6years

8years

10years

6

8

10

12

14

91days

4

marketrates

yield curve

x

x

x

x

x

x

x

xx

x

x

x

x

1.9 INTEREST RATES

Interest rates have their genesis in the money market, starting with the repo rate. The repo rate is made

effective by the existence of a borrowed reserves condition, which in South Africa is a permanent feature of

the financial landscape. The repo rate has an almost direct influence on the bottom end of the yield curve,

which may be depicted as in Figure 1.5.

The yield curve is a representation of the relationship between interest rates and term to maturity. The

money market is represented in the lower end of the yield curve and the bond market the part after one

year to maturity. Thus the bond market can be seen to be an extension of the money market.

1.10 THE DERIVATIVE MARKETS

The word “derivative” means that the product that it describes is “derived” from something. The

“something/s” are financial market instruments and indices (i.e. indices of prices and interest rates) of

financial instruments. This means that the derivatives cannot exist on their own, i.e. they piggyback on the

ordinary financial market instruments or indices. However, it must be rapidly added that there are

derivatives that piggyback on other derivatives. Examples are options on futures and options on swaps.

Derivatives are contracts between two parties to buy, sell or exchange (optional or obligatory) a standard or

non-standard quantity and quality of an asset or cash flow at a pre-determined price on or before a specified

date in the future. The value of the underlying security or index (the spot market instrument that underlies

the derivative) changes continuously, and this means that the value of the derivative almost always also

changes.

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For example, the value of a future on a share index changes as the index changes in value. Also, the value of

an option on a bond changes because the rate on the bond changes in the secondary market.

deriv’s deriv’s deriv’sderiv’s

debt market

SPOT FINANCIAL INSTRUMENTS / MARKETS

forexmarket

commodity markets

equity market

Figure 1.6: spot and derivative markets

SPOT COMMODITY MARKETS

The terminology of the derivative markets can be confusing (caps, floors, collars, options, futures, options on

futures, FRAs, repos, swaps, swaptions, and the like), and this leads to the need to categorise these markets

in a sensible fashion. The derivative markets may be broadly categorised according to:

• Commodity derivative markets.

• Financial derivative markets.

The term financial or financial markets refer to the debt, equity and forex markets. Thus, we can depict the

derivative markets as shown in Figure 1.6.

This broad categorisation makes sense because there is a fundamental difference between these markets in

terms of underlying assets and market turnover. The underlying assets in the commodities derivative

markets are various, such as gold, maize, oil, etc, which are fundamentally different to the financial assets or

notional financial assets that underlie financial derivatives. Turnover on the latter market dwarfs the

turnover on the former.

However, there is much overlap in terms of the types of derivatives that are found in both markets. For

example, in both market types forwards, futures, options, and swaps are to be found.

It may also make sense to categorise these markets according to whether they are:

• formalised derivative markets (i.e. exchange traded), as opposed to

• informal derivative markets (i.e. OTC).

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For example, there are formalised markets in futures and options on futures; and there are informal OTC

markets in forwards, interest rate caps and floors, forward rate agreements, interest rate and currency

swaps, etc. However, this is not the ideal categorisation because there are derivatives that have feet in both

the formal and the OTC markets (for example forward rate agreements).

Figure 1.7: derivative instruments / markets

OPTIONSOTHER(weather, credit, etc)

FUTURES

FORWARDS SWAPS

options on swaps =swaptions

options on

futures

forwards / futures on swaps

Another way in which one may categorise derivatives is according to the broad types of derivatives:

forwards, futures, options (which include options on futures and swaps), swaps, and other (such as credit

and weather derivatives). This classification may be depicted as in Figure 1.7.

However, this is not ideal because there is a need to relate them to the spot (cash) markets. This is shown in

Figure 1.8.

debt market


forexmarket

commodity markets

equity market

money market

bond market

Figure 1.8: derivatives and relationship with spot markets


FUTURES

FORWARDS SWAPS


options on

futures


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This illustration in Figure 1.8 is also not ideal because it cannot capture the finer distinctions of the derivative

markets (for example forwards actually do not apply to all the markets). Table 1.3 provides the detail of the

derivative markets and how they relate to the spot markets.

Even the classification offered in Table 1.3 is not foolproof, because further explanation is required in some

cases to make it absolutely clear. This type of information cannot be captured in an illustration or a table; it

requires explanation.

However, Figure 1.8 and Table 1.3 do provide an overarching view of the types of derivative instruments and

provides a logical framework for discussion. Taking the above as a cue, the following chapters are arranged

as follows:

• Forwards

• Futures

• Options

• Swaps

• Other

TABLE 1.3: SPOT MARKETS AND DERIVATIVE INSTRUMENTS

Derivatives Debt market Equity market Forex market Commodities

market

Forwards Yes Yes Yes Yes

Futures Yes Yes Yes Yes

Options

Options on “physicals”1

Yes Yes Yes Yes

Options on futures Yes Yes Yes Yes

Options on swaps Yes Yes Yes Yes

Warrants2

Yes Yes

Caps and floors Yes Yes

Swaps2

Yes Yes Yes Yes

Other

Credit derivatives

Do not apply to specific financial or commodity markets

Weather derivatives

Do not apply to specific financial or commodity markets

1. The actual spot market instruments and indices. 2. Requires explanation (done later).

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Each of the derivative instrument groups will be discussed in some detail in this document and, where

applicable, we cover the following detail:

• The product/s

• The mathematics

• The applications

• Organization of the market

• Participants

• Clearing and settlement

• The situation in South Africa at present

• Variations on the theme

1.11 REVIEW QUESTIONS AND ANSWERS

Outcomes

• Understand the context and basics of the derivative markets.

Self-test questions

1. Financial markets consist of four distinct markets: the debt markets, the equity market, the foreign

exchange market and the derivatives market. True or false?

2. Prices in derivatives markets are not as volatile as prices in spot markets. True or false?

3. Derivatives are found in both formalised (exchange) markets and informal (OTC) markets. True or false?

4. Define a 'derivative'?

Answers

1. False. Derivatives are found in all the financial markets and it is not a market on its own.

2. False. Derivatives derive their values from that of the underlying instruments and will therefore reflect

the changes in the prices of the latter.

3. True.

4. Derivatives are contracts between two parties to exchange a standard or nonstandard quantity and

quality of an asset or cash flow at a pre-determined price at a specified date in the future.

20

CHAPTER 2: FORWARDS




Chapter 2 Forwards

Chapter 3 Futures

Chapter 4 Swaps

Chapter 5 Options



After studying this chapter the learner should / should be able to:

• Understand the characteristics of forward markets.

• Understand the essence and mechanics of forward contracts / instruments.

• Understand the mathematics of the forward markets.

• Calculate a forward price.

• Know the advantages and disadvantages of forward markets vis-à-vis futures markets.

• Understand the organisational structure of the forward markets.

2.3 INTRODUCTION

The largest market in the category forward markets is the forward foreign exchange market. But there are

also other forward markets, such as forward markets in interest rate products and commodities. An

understanding of forward markets is required in order to understand futures, as they were the forerunners

of futures markets. The following are the sections covered in this chapter:

• Spot market

• Introduction to forward markets

• A simple example

• Forward markets

• Forwards in the debt markets

• Forwards in the foreign exchange market

• Forwards in the commodities markets

• Forwards on derivatives

• Organisation of forward markets

• Summary

• Review questions and answers

21

2.4 SPOT MARKET

The spot market is also called the “cash market”, and it refers to transactions or deals (which are contracts)

that are settled at the earliest opportunity possible. For example (see Figure 2.1), in the money market a

spot deal is where securities are exchanged for payment (also called delivery versus payment) on the day the

deal is struck (T+0) or the following day (T+1). In the South African bond market a spot deal is a deal done

now (day T+0) for settlement in 3 days’ time (T+3). In the South African equity market spot currently means

T+5.

T + 0(now)

T + 1 1day

T + 2 days

T + 3 days

T + 4 days

T + 5 days

Money market Bond market

Equity market

Forex market

Spot markets

Spot market = cash market = deal settled asap Derivative markets = deal settled in future at prices determined NOW

Time line

The future

T + 91 days

T + 180 days

Derivative markets

etc

Figure 2.1: settlement in spot / cash markets & derivative markets

The issue that determines the number after the “+” sign is essentially convenience. In the money market it is

convenient to settle now or tomorrow, because the market is of a wholesale nature and the securities are

kept in safe custody by banks in large metropolitan areas (or in a securities depository or are

dematerialized). In the equity market many individuals are involved that are spread across the county and,

therefore, it takes time for the securities to be posted / sent to the exchange. This of course changes with

dematerialization / immobilisation3.

A spot deal may thus be defined as a contract between buyer and seller, undertaken on T+0, for the delivery

of a security by the seller to the buyer and payment by the buyer to the seller in order to complete

settlement of the deal at time T+0 or T+ a few days, depending on convenience.

2.5 INTRODUCTION TO FORWARD MARKETS

A forward market is a market (essentially a primary market) where a deal on an asset is concluded now (T+0)

for settlement at a date in the future at a price / rate determined now. The settlement date is not a few days

after T+0 as in the case of spot transactions, but usually a month or a few months after T+0 (see Figure 2.1).

The motivation for such a deal is usually that the spot price that will prevail in the future is uncertain.

The best way to describe a forward deal is with an example. Consider a wheat farmer; he plants his crop now

and expects to reap the harvest in 3 months’ time. He knows the input cost, but he does not know what spot

price he will get for his harvested wheat in 3 months’ time. Thus, he has risk (uncertainty).

3 Dematerialisation means that scrip (physical certificates) no longer exist, while immobilisation means that scrip exists but is placed

in a scrip depository which holds them on behalf of the investors (usually this means one certificate).

22

The solution to his risk is a forward (or futures) market that will enable to sell his wheat forward, in other

words he would like to deal now (T+0) at a price agreed now (T+0) for delivery of the wheat in 3 months’

time (T+ 3 months) when he will be paid.

A forward deal in the financial markets is the same except that the instrument dealt in:

• has a term to maturity and

• may have an income (dividend on a share / interest on a bond).

A spot deal on a 3-month asset may be depicted as in Figure 2.2. A forward deal is where the price or rate on

an asset is determined now for settlement at some stage in the future. Some stage means other that spot. A

3-month forward deal on a 3-month asset may be depicted as shown in Figure 2.3.

Figure 2.2: spot deal on T+0 on 3-month asset

Security

Money

time line

T+0 T+1month

T+2months

T+3months

T+4months

T+5months

T+6months

• Price agreed & paid by buyer

• 3-month asset delivered

• Asset matures• Buyer repaid

Term of asset

Issuer of security

Buyer of security

Money

Issuer of security

Buyer of security

Security

Time line

T+0 T+1

month

T+2

months

T+3

months

T+4

months

T+5

months

T+6

months

• Forward price paid by buyer

• 3-month asset

delivered

• Asset matures • Buyer repaid

Term of asset

• Price agreed by buyer and seller for

3-month asset for settlement on T+3

months

Figure 2.3: forward deal on 3-month asset (settlement in T+3 months)

23

2.6 A SIMPLE EXAMPLE

A forward is a contract between a buyer and a seller that obliges the seller to deliver, and the buyer to

accept delivery of, an agreed quantity and quality of an asset at a specified price (now) on a stipulated date

in the future. A simple example may clarify this definition (see Figure 2.4).

“Prof it” for the buyer

“Loss” for the seller

T T+3

months

R100

R120

R110

R90

R103.74

Price

Time

Market (spot) price

R120.00

Figure 2.4: example of a forward deal

A forward transaction is effected on 18 September 2005 (T+0). On this day the spot price of a basket of

mielies (maize) is R100. A consumer (buyer) believes that the price of mielies (his favorite food) will be much

higher in three months’ time (because of an anticipated drought). He would thus like to secure a price now

for a basket of mielies he would like to purchase in three months’ time.

The farmer (producer and seller), on the other hand, believes that the price of mielies will decline (because

he anticipates plenty of rain). The farmer quotes the buyer a price of R103.74, i.e. he undertakes to supply

the buyer with one basket of mielies on 18 December (after 91 days) for a consideration (price) of R103.74.

This figure the farmer arrived at by taking into account the interest rate he is paying the bank for a loan used

to produce the mielies. Assuming the interest rate to be 15.0% pa, he calculates the forward price according

to the following formula (= cost of carry model):

FP = SP x [1 + (ir x t)]

where

FP = forward price

SP = spot price

t = term, expressed as number of days / 365

ir = interest rate per annum for the term (expressed as a unit of 1)4

4 The interest rate represents the cost to the farmer of holding a stock of mielies, referred to as the “cost of carry". As we will show

later, the rate used in calculations of the fair value price (FVP) of forwards / futures in the risk-free rate (rfr).

24

FP = R100 x [1 + (0.15 x 91 / 365)]

= R100 x (1.037397)

= R103.74.

The buyer draws up a contract, which both Mr. Farmer and he (Mr. Consumer) sign (see Box 1).

BOX 1: SIMPLIFIED FORWARD CONTRACT

FORWARD CONTRACT

18 September 2010

Mr. Consumer hereby undertakes to take delivery of, and Mr. Farmer hereby undertakes to deliver, one basket of

mielies on 18 December 2005 at a price of R103.74.

Signed

……………………… ………………………….

Mr. Farmer Mr. Consumer

On 18 December (after a drought) the price for a basket of mielies (i.e. the spot price) has risen to R120. The

consumer writes out a cheque for R103.74 in favour of the farmer, and takes delivery of the basket of

mielies. What is the financial position of each party to the forward contract?

The buyer pays R103.74. Had he waited until 18 December 2002 to purchase his basket of mielies, he would

have had to pay the spot price of R120. If, in the 91-day period, he had “gone off” mielies, he will still be

happy to purchase the basket at R103.74, and this is because he will sell the same basket at R120 (the spot

price now on 18 December). He thus profits to the extent of R16.26 (R120 – R103.74) (and is annoyed with

himself that he did not take a bigger “position”).

The farmer is unhappy because he could have sold the basket of mielies on 18 December for R120. This does

not mean that he made a loss. His production cost, including his carry cost, could only have been, say, R95.

He thus makes a profit of R8.74 (R103.74 – R95), but it is smaller than he would have made (R120 – R95.00

= R25) in the absence of the forward contract.

Had it rained and the supply of mielies increased, the price would have fallen. If we assume the price had

fallen to R90 per basket, the farmer is better off (received R103.74 as opposed to R90), whereas the buyer is

worse off (paid R103.74 as opposed to R90 had he not done the forward deal).

It is important at this stage to attempt to analyse the advantages and disadvantages of forward markets.

The main advantages that can be identified are:

25

• Flexibility with regard to delivery dates.

• Flexibility with regard to size of contract.

The disadvantages are:

• The transaction rests on the integrity of the two parties, i.e. there is a risk of non-performance.

• Both parties are “locked in” to the deal for the duration of the transaction, i.e. they cannot reverse

their exposures.

• Delivery of the underlying asset took place, i.e. there was no option of settling in cash.

• The quality of the asset may vary.

• Transaction costs are high (for example, the consumer visits the farmer at least twice, has a lawyer

to draw up the contract, etc).

2.7 FORWARD MARKETS

Futures markets developed out of forward markets because of the disadvantages of forward deals. However,

forward markets do still exist, and this is because of their advantages as mentioned above and the lack of the

disadvantages mentioned above in some markets. The following will make this clear:

• Flexibility with regard to delivery dates.


The transaction rests on the integrity of the two parties, but this is not a problem in certain markets where

the participants are substantive in terms e.g. capital and expertise (e.g. the Forex market).

Both parties are “locked in” to the deal for the duration of the transaction, but in certain markets they are

able to reverse their exposures with other instruments (e.g. futures in the Forex market).

Delivery of the underlying asset is the purpose of doing a forward deal in most cases (i.e. the client does not

want the option of settling in cash) (e.g. Forex market).

The quality of the asset does not vary in many cases (e.g. Forex market).

Transaction costs are not high in certain markets (e.g. Forex market because of high degree of liquidity).

As will have been guessed, the largest forward market is the forward foreign exchange market. In addition,

forward markets exist in the debt market, the equity market and in the commodities market. This means

that there are forward markets in all the financial markets.

In addition to the forwards that exist in all the financial markets there are also forwards on one of the

derivatives, i.e. swaps. The forward markets are discussed under the following sections:

• Forwards in the debt markets.

• Forwards in the equity market.

• Forwards in the foreign exchange market.

• Forwards in the commodity markets.

• Forwards on derivatives.

26

2.8 FORWARDS IN THE DEBT MARKETS

2.8.1 Introduction

The forward market contracts that are found in the debt markets are:

• Forward interest rate contracts.

• Repurchase agreements.

• Forward rate agreements.

2.8.2 Forward interest rate contracts

Introduction

A forward interest rate contract (FIRC) is the sale of a debt instrument on a pre-specified future date at a

pre-specified rate of interest. This category includes forwards on indices of interest rate instruments (such as

forwards on the GOVI index). Below we provide examples of FIRCs in the OTC market and the exchange-

traded markets:

• Example: OTC market.

• Examples: exchange-traded markets.

Example: OTC market

An example is probably the best way to describe the forward market in interest rate products, i.e. forward

interest rate contracts. As noted, these contracts involve the sale of a debt instrument on a pre-specified

future date at a pre-specified rate of interest, and contain details on the following:

• The debt instrument/s.

• Amount of the instrument that will be delivered.

• Due date of the debt instruments.

• Forward date (i.e. due date of the contract).

• Rate of interest on the debt instrument to be delivered.

IFR = 7.862% pa

Settlement date

Time line

T+0 T+ 100 days

T+ 306 days

Deal date

Figure 2.5: example of forward interest rate contract

206 days

Spot rate = 5% pa

Spot rate = 7% pa

27

An insurance company requires a R100 million (plus) 206-day negotiable certificate of deposit (NCD)

investment in 100 days’ time when it receives a large interest payment. It wants to secure the rate now

because it believes that rates on that section of the yield curve are about to start declining, and it cannot

find a futures contract that matches its requirement in terms of the exact date of the investment (100 days

from now) and its due date (306 days from now)

It approaches a dealing bank and asks for a forward rate on R100 million (plus) 206-day NCDs for settlement

100 days from now. The spot rate (current market rate) on a 306-day NCD is 7.0% pa and the spot rate on a

100-day NCD is 5% pa. It will be evident that the dealing bank has to calculate the rate to be offered to the

insurer from the existing rates. This involves the calculation of the rate implied in the existing spot rates, i.e.

the implied forward rate (IFR) (see Figure 2.5):

IFR = {[1 + (irL x tL)] / [1 + (irS x tS)] – 1} x [365 / (tL – tS)]

where

irL = spot interest rate for the longer period (306 days)

irS = spot interest rate for shorter period (100 days)

tL = longer period, expressed in days / 365) (306 / 365)

tS = shorter period, expressed in days / 365) (100 / 365)

IFR = {[1 + (0.07 x 306 / 365)] / [1 + (0.05 x 100 / 365)] –1} x 365 / 206

= [(1.05868 / 1.01370) –1] x 365 / 206

= (1.04437 – 1) x 365 / 206

= 0.07862

= 7.862% pa.

The bank will quote a rate lower than this rate in order to make a profit. However, we assume here, for the

sake of explication, that the bank takes no profit on the client. It undertakes to sell the NCDs to the insurer

at 7.862% pa after 100 days.

The financial logic is as follows5: the dealing bank could buy a 306-day NCD from another bank and sell it

under repo (have it “carried”) for 100 days; the repo buyer will earn 5.0% pa for 100 days and the ultimate

buyer, the insurer (the forward buyer), the IFR of 7.862% pa for 206 days. The calculations follow:

The dealing bank buys R100 million 306 day NCDs at the spot rate of 7.0% pa. The interest = 7.0 / 100 x R100

000 000 x 306 / 365 = R5 868 493.15.

The maturity value (MV) of the investment = cash outlay + interest for the period = R100 000 000 + R5 868

493.15 = R105 868 493.15.

5 Based on the" arbitrage principle", ie if this were not the rate, arbitrage could take place.

28

The bank has the NCDs “carried” for 100 days at the spot rate for the period of 5.0% pa. This means it sells

the R100 million NCDs at market value (R100 million) for a period of 100 days at the market rate of interest

for money for 100 days.

After 100 days, the bank pays the “carrier” of the NCDs interest for 100 days at 5.0% pa on R100 million =

R100 000 000 x 5.0 / 100 x 100 / 365 = R1 369 863.01.

The bank now sells the NCDs to the insurer at the IFR of 7.862% pa. The calculation is: MV / [1 + (IFR / 100 x

days remaining to maturity / 365)] = R105 868 493.15 / [1 + (7.862 / 100 x 206 / 365)] = R101 370 498.00.

The insurer earns MV – cash outlay for the NCDs = R105 868 493.15 – R101 370 498.00 = R4 497 995.10 for

the period.

Converting this to a pa interest rate: [(interest amount to be earned / cash outlay) x (365 / period in days)] =

[(R4 497 995.10 / R101 370 498.00) x (365 / 206)] = 7.862% pa, i.e. the agreed rate in the forward contract.

Essentially what the dealing bank has done here is to hedge itself on the forward rate quoted to the insurer.

It will be evident, however, that the bank, while hedged, makes no profit on the deal. As noted, in real life

the bank would quote a forward rate lower than the break-even rate of 7.862% pa (e.g. 7.7% pa.)

The principle involved here, i.e. “carry cost” (or “net carry cost” in the case of income earning securities), is

applied in all forward and futures markets. This will become clearer as we advance through this module.

The above is a typical example of a forward deal in the debt market. It will be apparent that the deal is a

private agreement between two parties and that the deal is not negotiable (marketable). The market is not

formalised and the risk lies between the two parties. It is for this reason that the forward interest rate

contract market is the domain of the large players, and these are the large banks, and the institutions6.

Numbers in respect of OTC FIRCs are not available.

2.8.3 Repurchase agreements

Introduction

A knowledgeable student will have noted that the above deal (the OTC FIRC) could have been executed by

the insurer by way of the celebrated repurchase agreement (repo). The insurer could have bought the bonds

outright and sold them to some other holder of funds under repo for the relevant period. Similarly the bank

could have bought the bonds and sold them under repo instead of taking in a deposit to fund them. The repo

is just another way of funding an asset.

In most international textbooks, the repo is not covered under derivative instruments, but is rather regarded

as a money market instrument. We regard the repo as a derivative because it is derived from money or bond

market instruments, and its value (i.e. the rate on it) is derived from another part of the money market (the

price of money for the duration of the repo).

6 The term “institutions” is used loosely in the financial markets to apply to the large investors, ie the retirement funds, insurers and

securities unit trusts.

29

The repo may also be seen as a combination of a spot and a forward transaction, specifically a spot sale and

a simultaneous forward purchase of the same instrument (from the point of view of the seller / maker). The

buyer of the repo does a simultaneous spot purchase and forward sale.

The repo may also be regarded as a short-term loan secured by the assets sold to the lender. Another way of

putting this is that the repo is similar to a collateralised loan in that the purchaser of the securities under

repo is providing funds to the seller and its loan is backed by the securities for the period of the agreement;

the lender receives a return based on the fixed price of the agreement when it is reversed.

The repo is discussed in much detail here because it is a versatile instrument and the market in this

instrument is vast. The sections we cover here are:

• Definition

• Terminology

• Example

• Purpose of effecting repurchase agreements

• Participants in the repurchase agreement market

• Types of repurchase agreements

• Securities that underlie repurchase agreements

• Size of repurchase agreement market

• Mathematics of repurchase agreements

• Repos and the banking sector

• Listed repurchase agreements

Definition

A repurchase agreement (repo) is a contractual transaction in terms of which an existing security is sold at its

market value (or lower) at an agreed rate of interest, coupled with an agreement to repurchase the same

security on a specified, or unspecified, date. This definition perhaps requires further elaboration.

Agreement

The transaction note confirming the sale of the security can contain a note stipulating the agreement to

repurchase. Alternatively, two transaction notes can be issued, i.e. a sale note together with a purchase note

dated for the agreed repurchase date. It is market practice that underlying all repurchase agreements is the

TBMA / ISMA Global Master Repurchase Agreement, (GMRA), i.e. an internationally recognised repo

contract.

Existing security

The maker of the repo sells a security already in issue to the buyer of the agreement.

30

Market value

The security is sold at its market value (and sometimes at better, i.e. lower, than market value), in order to

protect the buyer of the repo against default of the maker. If the seller fails to repurchase the security at

termination of the repo, the holder acquires title to it and has the right to sell it in the market. For example,

if the value of the securities sold is R9 500 000, the repo is done at a value of R9 450 000, and the interest

factor for the period of the repo is R35 000 (total = R9 485 000), the buyer is protected should the maker

default.

Agreed rate of interest

The agreed rate for the term of the agreement is the interest rate payable on the repo by the seller for the

relevant period. This applies in the case where the maturity date of the agreement is specified. A small

number of repos are “open repos”, i.e. both the buyer and the seller have the right to terminate the

agreement at any time. The rate payable on these open repos is a rate agreed between the two parties to

the deal; the rate may be benchmarked or it may be agreed daily.

Specified maturity date

The specified maturity date is the date when the agreement is terminated. The buyer sells the security /

securities underlying the repo back to the maker for the original consideration plus the amount of the

interest agreed.

Unspecified maturity date

In the case of an agreement where the maturity date is not specified (the open repo), the termination price

(original consideration plus interest) cannot be agreed at the outset of the agreement. The rate at which

interest is calculated can be fixed or floating, but is usually the latter. In the case of a floating rate, as noted,

the rate would be an agreed differential below or above a benchmark rate.

Terminology

The terminology related to repo is often confusing to those not involved in the money market. The term

repurchase agreement applies to the seller of the agreement. He agrees to repurchase the security. The

buyer of the agreement, on the other hand, is doing a resale agreement. He agrees to resell the security to

the maker of the agreement.

Synonyms for the repurchase agreement are buy-back agreement (point of view of the maker) and sell-back

agreement (point of view of the buyer). Repurchase agreements are also frequently referred to warehousing

transactions. The seller is doing a warehousing transaction and the buyer is warehousing an asset.

Terminology also used by some participants is repo-in and repo-out. The former is a resale agreement and

the latter a repurchase or buy-back agreement. Both makers and buyers, however, sometimes use the word

carry. The maker would say he is having securities carried, while the buyer would say he is carrying

securities.

The terminology used by the Reserve Bank in its accommodation procedures and open market operations is

also a challenge. The Bank accommodates the banks by doing repos at the repo rate. What the Bank is

actually doing is resale agreements with the banks. The banks are doing repurchase agreements with the

Reserve Bank.

31

At times the Reserve Bank sells securities to the banks to “mop up” liquidity, i.e. to increase the money

market shortage. It refers to these as reverse repos. In fact, they are not reverse repos from the Reserve

Bank’s point of view; they are repos.

Similarly, when the Bank sells foreign exchange to the banks in order to “mop up” liquidity, it says it does

Forex swaps with the banks. This is true, but the transactions may be seen to be repurchase agreements

with the banks in foreign exchange at the money market rate, less the relevant foreign interest rate for the

term of the repo. This is discussed in detail later.

The majority of participants and certainly the central bank mainly use the term repo, and we will acquiesce

in this regard, but use the correct terminology where appropriate to avoid confusion.

Example

T+0(issuedate)

T+30 T+100 T+ 360(maturity

date)

70-day repo

R10 million 360-day NCD

Time line

Figure 2.6: example of repo

Figure 2.6 provides an example of a repo deal. A bank has in portfolio a R10 million NCD of another bank that

it is holding in order to make a capital profit when rates fall. The NCD had 360 days to maturity when it was

purchased. It is now day 30 in the life of the NCD (i.e. it has 330 days to run), and the bank needs funding for

a particular deal that has 70 days to run. The bank sells the NCD to a party that has funds available for 70

days under agreement to repurchase the same NCD after 70 days. The rate agreed is the market interest

rate for 70 days.

Motivation for repos

One of the main reasons which give rise to repos is best described by way of an example. A client of a

broker-dealer may wish to invest R50 million for a 7-day period. If the broker-dealer cannot find a seller of

securities with a term of 7 days, he will endeavour to find a holder of securities who requires funds for this

period. If the rate for the repurchase agreement can be agreed, the broker would effect a resale agreement

with the seller of the securities and a repurchase agreement with the buyer.

Another way of putting this is that the seller is having the broker carry his securities for a period, while the

broker is having these same securities carried by the buyer for the same period. Another reason which gives

rise to repurchase agreements is holders of securities requiring funds for short-term periods.

Yet another transaction that gives rise to a repo is the taking of a position in a security. For example, a

speculator who believes that bond rates are about to fall (say in the next week) would buy, say, a 5-year

bond to the value of, say, R5 million at the spot rate of, say, 9.5% (the consideration of course will not be a

nice round amount).

32

He does not have the funds to undertake this transaction, but has the creditworthiness to borrow this

amount in the view of a broker-dealer. The speculator would thus immediately sell the bond to the broker-

dealer (who is involved in the repo market) for 7 days at 10.2% pa (the rate for 7-day money). The broker-

dealer in turn would on-sell the bond to, say, a pension fund for 7 days at, say, 10.0% pa.

Assume now that the 5-year bond rate falls to 9.4% on day seven. The broker-dealer unwinds the repo deal

and pays the pension fund R5 million plus interest at 10% for 7 days (R5 000 000 x 7 / 365 x 0.10 = R9

589.04). The broker-dealer then sells the bond back to the speculator for R5 million plus interest at 10.2%

(R5 000 000 x 7 / 365 x 0.102 = R9 780.82). The broker’s profit is 0.2% on R5 million for 7 days (i.e. the

difference between the two above amounts (R191.78).

The speculator sells the bond in the bond market at 9.4% (remember he bought it at 9.5%). His profit on the

5-year-less-7-days bond is 0.1% (which is probably around R50 000 – we assume this), i.e. the consideration

on the bond is R5 000 000 + R50 000 = R5 050 000. His overall profit is thus R50 000 minus the cost of the

carry (R9 780.82), i.e. R40 219.18.

SPECULATORPENSION

FUND

BROKER-DEALER

SELLEROF

BOND

Bond Bond

R5millionR5million

Bond R5million

Figure 2.7: cash and security flows at onset of repo

This deal may be depicted as in Figure 2.7 and Figure 2.8.

Figure 2.8: cash and security flows on termination of repo

SPECULATORPENSION

FUND

BROKER-DEALER

NEW BUYEROF

BOND

Bond Bond

R5millionR5million

Bond R5.05million

R9 780.82 R9 589.04

33

It will be evident that the speculator sold his bond position to the broker under repurchase agreement for 7

days (or had them carried for this period). The broker did a resale agreement for 7 days with the speculator

(or carried the bonds), and a repurchase agreement with the pension fund (or had the bonds carried by the

pension fund). The pension fund did a resale agreement with the broker, or carried the bonds for 7 days.

Another rationale for the repo market is the interbank market. This is covered in the following section.

Institutions involved in the repo market

The above are the main reasons that give rise to repurchase agreements, i.e. a party wishing to acquire

funds for a period and a party with a matching investment requirement. And there are many strategies that

underlie these agreements.

The parties involved in this market are the money market broker-dealers, the banks, corporate entities,

pension funds, insurance companies, money market funds, the Reserve Bank, foreign investors, speculators

in the bond market, etc.

Of all these institutions, the Reserve Bank and the banks are the largest participants, because the repo is the

method used by the Reserve Bank to provide accommodation to the banks (see below).

Types of repurchase agreements

As noted earlier, there are two main types of repurchase agreements, i.e. the open repurchase agreement

and the fixed term repurchase agreement. The former agreement is where there is no agreed termination

date. Both parties have the option to terminate the agreement without notice. The rate on these

agreements is usually a floating rate, the basis of which is agreed in advance.

Fixed term repurchase agreements are repurchase agreements where the rate and the term are agreed at

the outset of the agreement. The term of repos usually range from a day to a few months.

Securities that underlie repos

Only prime marketable securities are used in repos, and this includes money market and bond market

securities. Repos are usually done at market value of the underlying securities or lower than market value,

and the securities are rendered negotiable. Securities are rendered negotiable to protect the investor against

the maker of the repo, i.e. in the event of the maker reneging on a deal, the investor has the right to sell the

underlying securities (in terms of the ISDA Master Repurchase Agreement).

What is meant by rendered negotiable is that the underlying securities are prepared in negotiable form. For

example, a bank acceptance made payable to a particular investor is endorsed in blank. In the case of bond

certificates this means that a signed securities transfer form accompanies each certificate.7

7 Certificates are only applicable in markets where dematerialisation or immobilisation has not been implemented.

34

Size of repo market

It is unfortunate that no data are available on the size of the repurchase agreement market. The market size

is estimated to be in the region of R30 billion to R50 billion, i.e. the outstanding value of repurchase

agreements at any point is between these numbers. This is not an unreasonable range when it is considered

that the repos between the Reserve Bank and the banks are often in excess of R15 billion.

It should also be recollected that the foreign sector is at times a huge holder of bonds and equities, much of

which is carried in the local money market. Also, there are many speculators in the local bond market. Proof

of this is found in the mammoth turnover in the bond market. It is often contended by some that the South

African bond market is one of the most liquid in the world.

Mathematics of the repurchase agreement market

Repurchase agreements are dealt on a yield basis, i.e. the interest rate is paid on an add-on basis. The

amount of interest is calculated in terms of the following formula:

IA = C x ir x t

where

IA = interest amount

C = consideration (i.e. the market value or lower of the securities)

ir = agreed interest rate per annum expressed as a unit of 1

t = term of the agreement, expressed in days / 365

If, for example, R10 million (nominal value) NCDs with a maturity value of R10 985 000, and a market value

of R10 300 000, were sold for seven days at a repo rate of 12.0% pa, the interest payable would be as

follows:

IA = C x ir x t

= R10 300 000 x 0.12 x 7 / 365

= R23 704.11.

It should be clear that the buyer would pay R10 300 000 for the repo and receive R10 323 704.11 upon

termination of the agreement.

Repos and the banking sector

Because the banks are the largest initiators of repos, and a large slice of the market takes place between

banks, it is necessary to afford this sector a separate section.

Because repos are one method through which banks are able to acquire funding, the Reserve Bank requires

banks to report on balance sheet all their repos, for purposes of their capital adequacy requirement, i.e.

banks are required to allocate capital to this activity (because the asset has to be bought back). It will be

evident that if a bank brings back on balance sheet securities sold, it has to create a liability, and this liability

item is termed “loans under repurchase agreements”.

35

There are many reasons for banks engaging in the repo market. Perhaps the most prominent is that the repo

instrument is a convenient method to satisfy wholesale clients’ needs (retail clients do not feature in this

market).

All the major banks have Treasury Departments, and this department is the hub of these banks. All

wholesale transactions and portfolio planning take place in the Treasury Department.

If a large mining house client, for example, would like to purchase R100 million securities that have 63 days

to run (because it need the funds for an acquisition in 63 days’ time and is “full”8 in terms of its limit for the

bank), the bank is able to satisfy the client’s investment requirement by selling R100 million of its strategic

holding of government bonds to the client for 63 days.

Another example is a small bank losing a R100 million deposit at the end of the trading day, and not being

able to negotiate a deposit to fund the shortfall with the non-bank sector. Assuming a large bank has a R100

million surplus, and that this bank does not want to be exposed to the small banks, it may offer the R100

million to the small bank against a repo, i.e. the small bank will sell securities to the value of R100 million to

the large bank for a day or two (at the rate for this period). Clearly, if the small bank fails in this period, the

large bank has claim to the repo securities.

In South Africa, banks are accommodated by the Reserve Bank effecting repos with them, i.e. the banking

sector sells eligible securities to the Reserve Bank under repo. The style of monetary policy adopted in South

Africa is ensuring that the banks are indebted to the Reserve Bank at all times (i.e. borrow cash reserves on a

permanent basis), in order to “make repo rate effective”. These repos between the banks and the Reserve

Bank presently amount to over R14 billion every day (on average).

Listed repurchase agreements

Generally speaking, the repo market is an OTC market. However, repos on bonds are widely-used

instruments; thus a listed repo was created (in 2004) by Yield-X (JSE). It is called a j-Carry and is simply a repo

(or carry) on a specific bond. J-Carries are available on all the bonds listed on Yield-X, and have tenors for 1-

13 weeks.

The mathematics of repos in the case of bonds is similar to that of bond forwards (remember a repo is a

combination of a spot sale and a forward purchase). The carry rate is applied to the all-in price at the first

settlement date of the deal (called reference price) to determine the price at termination (second

settlement date).9

8 In terms of credit risk management practices, companies have limits on their exposure to individual banks (and other institutions).

9 A calculator for such transactions is provided by BESA at: http://calculator.bondexchange.co.za/

36

2.8.4 Forward rate agreements

General

A forward rate agreement (FRA) is an agreement that enables a user to hedge itself against unfavourable

movements in interest rates by fixing a rate on a notional amount that is (usually) of the same size and term

as its exposure that starts sometime in the future. It is akin to a foreign exchange forward contract in terms

of which an exchange rate for a future date is determined upfront.

Fixed interest rate

T+ 1 month

Settlement date

Time line

T+0 T+ 2 months

T+ 3 months

T+ 4 months

T+ 5 months

T+ 6 months

Deal date

Figure 2.9: 3 x 6 FRA

An example is a 3 x 6 FRA (3-month into 6-month): the 3 in the 3 x 6 refers to 3 months’ time when

settlement takes place, and the 6 to the expiry date of the FRA from deal date, i.e. the rate quoted for the

FRA is a 3-month rate at the time of settlement. This may be depicted as in Figure 2.9.

This type of instrument is particularly useful for the company treasurer who is of the opinion that the central

bank is about to increase the repo rate and that the interest rates on commercial paper (his borrowing

habitat) will rise sharply. He needs to borrow R20 million in three months’ time for a period of three months.

He approaches a dealing bank that he normally deals with on 4 March and obtains quotes on a series of FRAs

as shown in Table 2.110.

TABLE 2.1: FICTIONAL FRA QUOTES

FRA Bid (% pa) Offer (% pa) Explanation

3 x 6

6 x 9

9 x 12

10.00

10.20

10.40

10.10

10.30

10.50

3-month rate in 3 months’ time



The treasurer verifies these rates against the quoted FRA rates of another two banks (i.e. to ensure that he is

getting a good deal), finds that they are fair and decides to deal at the 10.10% pa offer rate for the 3 x 6 FRA for

an amount of R20 million, which matches the company’s requirement perfectly. The applicable future dates

are 4 June and 3 September (91 days).

10 Certain banks act as market makers in FRAs.

37

The transaction means that the dealing bank undertakes to fix the 3-month borrowing rate in three months’

time at 10.10% for the company. The transaction is based on a notional amount of R20 million. The notional

amount is not exchanged; it merely acts as the amount upon which the calculation is made.

The rate fixed in the FRA is some benchmark (also called reference) rate, or a rate referenced on a benchmark

rate, i.e. some rate that is readily accepted by market participants to represent the 3-month rate. We assume

this is the 3-month JIBAR rate, which is a yield rate.

On settlement date, i.e. 4 June, the 3-month JIBAR rate is 10.50% pa. On this day the 3-month (91-day)

commercial paper rate is also 10.50% pa (which it should be because the JIBAR rate is representative of the 3-

month rate). The company borrows the R20 million required at 10.50% through the issue of commercial paper

for 91 days. According to the FRA the dealing bank now owes the company an amount of money equal to the

difference between the spot market rate (i.e. 3-month JIBAR = 10.50% pa) and the agreed FRA rate (i.e. 10.10%

pa) times the notional amount. This is calculated as follows:

SA = NA x ird x t

where

SA = settlement amount

NA = notional amount

ird = interest rate differential (10.50% pa - 10.10% pa = 0.40% pa)

t = term (forward period), expressed as number of days / 365

SA = R20 000 000 x 0.004 x (91 / 365)

= R19 945.21.

Note that this formula applies in the case where settlement of this amount is made in arrears at month 6 (= 3

September). If the amount is settled at month 3 (= 4 June) it has to be discounted to present value (PV). The

discount factor is:

df = 1 / [1 + (rr x t)]

where

rr = reference rate (= JIBAR rate)

t = term of agreement (number of days / 365)

df = 1 / [1 + (rr x t)]

= 1 / [1 + (0.105 x 91 / 365)]

= 0.97449.

Therefore (PVSA = present value of settlement amount):

PVSA = SA x df

= R19 945.21 x 0.97449

= R19 436.41

38

This transaction may be illustrated as in Figure 2.10. It will be evident that the exchange of interest on R20

million does not take place; the dealing bank only settles the difference.

Figure 2.10: example of FRA: bank settles difference

LENDER (BUYER OF

COMMERCIAL PAPER)

BORROWING COMPANY

Market rate (10.5% pa)

FRA agreed rate (10.1% pa)

Market rate (10.5% pa)

DEALING BANK

Dif ference settled (10.5% pa – 10.1% pa) x R20 million x discount

factor

Money

Implied forward rate

Figure 2.11: money market yield curve

implied rate = 11.74%

1

month

Time line

1

day

2

months

3

months

4

months

5

months

6

months

7.0% 8.0% 8.5% 9.0% 9.5% 10.0% 10.5%

The dealing bank would of course not have sucked the rates quoted out of thin air. It would have based its

forward rates on the rates implicit in the spot market rates. An example is required (see Figure 2.11).

Shown here are the spot rates for various periods at a point in time11. This may also be called a money

market yield curve (as opposed to a long-term yield curve which stretches for a number of years). This

notional yield curve may also be depicted as in Figure 2.12 (this is an unrealistic yield curve, because the

yield curve does not usually follow straight lines).

11 It depicts a normally shaped yield curve.

39

Figure 18: fabricated money market yield curve

1 day

1 month

2 months

3 months

4 months

5 months

6 months

7.0

9.0

9.5

8.5

8.0

7.5

10.0

10.5

term to maturity

% pa

Figure 2.12: fabricated money market yield curve

The rate now (spot rate) for three months is 9.0% pa and the rate now (spot rate) for six months is 10.5% pa,

and we know that the latter rate covers the period of the first rate. The rate of interest for the three-month

period beyond the three-month period can be calculated by knowing the two spot rates mentioned. This is

the forward rate of interest, or the implied forward rate. This is done as follows (assumption 3-month

period: 91 days; 6-month period: 182 days):


where

IFR = implied forward rate

irL = spot interest rate for the longer period (i.e. 6-month period)

irS = spot interest rate for shorter period (i.e. 3-month period)

tL = longer period, expressed in days / 365) (i.e. the 6-month period -182 days)

tS = shorter period, expressed in days / 365) (i.e. 3-month period - 91 days)

IFR = {[1 + (0.105 x 182/365)] / [1 + (0.09 x 91/365)] –1} x 365/91

= [(1.0524 / 1.0224) –1] x 365/91

= (1.0293 – 1) x 365/91

= 0.1174

= 11.74% pa.

40

The bank, in the case of a 3 x 6 FRA, will quote a rate that is below the implied 3-month forward interest

rate, i.e. below 11.74%.

2.9 FORWARDS IN THE EQUITY MARKET

There is only one type of forward contract in the equity market, and this is the outright forward. An outright

forward is simply the sale of equity at some date in the future at a price agreed at the time of doing the deal.

The mathematics is straightforward (= cost of carry model):

FP = SP x [1 + (ir x t)]

where

FP = forward price

SP = spot price


ir = interest rate per annum for the term (expressed as a unit of 1).

An example is required: a pension fund believes the price of Company XYZ shares will increase over the next

85 days when its cash flow allows the purchase of these shares. It requires 100 000 shares of the company

and approaches a broker-dealer to do an 85-day forward deal. The broker-dealer buys the 100 000 shares

now at the spot price of R94 per share and finances them by borrowing the funds from its banker at the

prime rate of 12.0% pa for 85 days. It offers the pension fund a forward deal based on the following

(assumption: non-dividend paying share):

SP = 100 000 shares of Company XYZ at R94.0 per share = R9 400 000

t = 85 days

ir = 12.5% = 0.125 (note that the it includes a margin of 0.5%)

FP = R9 400 000 x [1 + (0.125 x 85 / 365)]

= R9 400 000 x 1.029110

= R9 673 634.00.

After 85 days the pension funds pays the broker-dealer this amount for the 100 000 Company XYZ shares,

and the broker-dealer repays the bank:

Consideration = R9 400 000 x [1 + (0.12 x 85 / 365)]

= R9 400 000 x 1.027945

= R9 662 684.92.

The broker-dealer makes a profit of R10 949.07 (R9 673 634.00 – R9 662 684.92).

Clearly, the pension fund at the start of the deal is of the opinion that the price of the shares will increase by

more than the price of money for the period. Pension funds mainly do outright forward equity transactions

and this is because they are not permitted to incur borrowings. The pension fund would also “shop around”

to find the best deal.

41

2.10 FORWARDS IN THE FOREIGN EXCHANGE MARKET

2.10.1 Introduction

Foreign exchange is deposits and securities in a currency other than the domestic currency, and an exchange

rate is an expression of units of a currency in terms of one unit of another currency. An example is USD / ZAR

7.5125, which means that ZAR 7.5125 is required to buy USD 1.012. The 1.0 is left out of the expression

because it is known to be 1.0. The one unit currency is called the base currency and the other the variable

currency.

There are two broad types of deals in foreign exchange, spot and forward, and there are four types of

forwards. The five deal types in foreign exchange are:

• Spot foreign exchange transactions.

• Forward foreign exchange transactions:

• Outright forwards.

• Foreign exchange swaps (not to be confused with “proper” currency swaps).

• Forward-forwards.

• Time options (not to be confused with “normal” options).

A spot foreign exchange transaction is a deal done now (on T+0) for settlement on T+2 (an international

convention), and essentially amounts to the exchange of bank deposits in two different countries.

Investments or the purchase of goods then occur as a second phase, i.e. the foreign bank deposit is used to

buy the foreign investment or goods. A forward foreign exchange transaction is a transaction that takes

place (i.e. is settled) on a date in the future other than the spot settlement date of T+2, but the price and

amount is agreed on the deal date (i.e. now – T+0). This transaction is called an outright forward. This type of

forward foreign exchange transaction and the other slight variations on the main theme are discussed

next.13

2.10.2 Outright forwards

Introduction

As noted, outright forwards are forward foreign exchange contracts, i.e. contracts between the market

making banks14 and clients, and may be defined as contracts in terms of which the banks undertake to

deliver a currency or purchase a currency on a specified date in the future other than the spot date, at an

exchange rate agreed upfront. The formula is:

12 Many authors prefer to write this example as: ZAR 7.5125 / USD 1.0 or simply as R/$ 7.5125, meaning rand per dollar. Note that

with this format the “/” in USD / ZAR is not a mathematical sign.

13 Note that these forwards are merely touched upon here because the detail is covered in the foreign exchange market module.

14 “Market making banks” refers to the fact that the foreign exchange market is “made” by the banks; they quote bid and offer

exchange rates simultaneously at all times in response to the approaches of clients (importers, exporters, etc).

42

Outright forward = SP x {[1 + (irvc x t)] / [1 + (irbc x t)]}

where

SP = spot exchange rate

irvc = interest rate on variable currency

irbc = interest rate on base currency

t = term, expressed as number of days / 365.

The above is the standard formula, because the vast majority of forwards are done for standard periods of

less than a year (30-days, 60-days, 90-days, 180-days, etc). When the period is longer than a year, the

formula becomes:

Outright forward = SP x [(1 + irvc)n / (1 + irbc)

n]

where n = number of years

(where the period is broken years, for example 430 days, then n = 430 / 365).

It will have been noted that the principal here is the PV / FV concept, with the difference being that there

are two interest rates that are to be taken into account. If the rate on the variable currency is higher than

the rate on the base currency, then the units of the variable currency will be higher, i.e. it takes more ZAR to

buy one USD on a forward date. Conversely, it takes less USD to buy one ZAR on the forward date. An

example is called for.

Example one

Forward period = 60 days

Spot rate = USD / ZAR 7.50

irbc = 5.0%pa

irvc = 10.0% pa

Outright forward rate15 = SP x {[1 + (irvc x t)] / [1 + (irbc x t)]}

= 7.50 x {[1 + (0.10 x 60/365)] / [1 + (0.05 x 60/365)]}

= 7.50 x (1.01643836 / 1.00821918)

= 7.56114134

= USD / ZAR 7.56114134.

Let us test the logic. An investor has the choice of investing in a ZAR 60-day deposit at 10.0% pa or in a USD

60-day deposit at 5.0% pa. In the former case the investor will earn (assuming ZAR 10 000 000 is available to

invest):

15 Note here that we increase the number of decimals (from the market norm) for purposes of demonstrating the principle.

43

Forward consideration = present consideration x [1 + (irvc x 60/365)]

= ZAR 10 000 000 x [1 + (0.10 x 60/365)]

= ZAR 10 000 000 x 1.01643836

= ZAR 10 164 383.60

In the latter case the investor buys the USD equivalent of ZAR 10 000 000 = USD 1 333 333.33 [ZAR 10 000

000 x (1 / 7.5)]. The investor immediately deposits this amount for 60 days at 5.0% pa, and sells the USD

forward consideration forward for ZAR at the forward rate of USD / ZAR 7.56114134:

Forward consideration = present consideration x [1 + (irbc x 60/365)]

= USD 1 333 333.33 x [1 + (0.05 x 60/365)]

= USD 1 333 333.33 x 1.00821918

= USD 1 344 292.23.

ZAR equivalent at forward exchange rate:

= USD 1 344 292.23 x 7.56114134

= ZAR 10 164 383.60.

It should be evident that the forward exchange rate may be calculated by dividing the ZAR forward

consideration by the USD forward consideration:

ZAR 10 164 383.60 / USD 1 344 292.23 = 7.5611.

Conclusion: the investor earns the same return in both countries, and this is so because of the principle of

interest rate parity:

The net rate of return from an investment offshore should be equal to the interest earned minus or plus the

forward discount or forward premium on the price of the foreign currency involved in the transaction.

This says that the interest differential between two currencies is related to the forward discount or

premium, and that interest rate parity is reached when the interest rate differential is equal to the discount

or premium on one of the currencies. In this example USDs are selling at a premium in the forward market

(think: more ZAR per USD in the forward market).

This condition in the forward market is brought about by arbitrage. The many participants in the foreign

exchange market seek out arbitrage opportunities in this regard (mispricing) and drive the forward exchange

rate to reflect the condition of interest rate parity.

In the above example the spot exchange rate was USD / ZAR 7.5 and the forward exchange rate USD / ZAR

7.5611 (rounded). Thus the forward points (or forward swap points) are 611 (or ZAR 0.0611). This is clarified

in the following section on foreign exchange swaps.

44

Example two

It will be useful to provide another example in order to clarify the PV/FV concept:

A South African borrows funds for 6 months from a South African bank, buys USD at the spot rate, invests

immediately in a 60-day USD deposit, and converts the USD forward consideration into ZAR at the forward

rate. The elements of the transactions are:

Amount borrowed = ZAR 10 000 000

ZAR borrowing rate = 10.0% pa

Spot exchange rate = USD / ZAR 7.5

USD 6-month deposit rate = 5% pa

Forward exchange rate = 7.56114134.

ZAR 10 000 000 at spot rate

= USD 1 333 333.33 (ZAR 10 000 000 / 7.5)

USD 1 333 333.33 at 5% pa for 60 days

= USD 1 333 333.33 x (1 + 0.05 x 60 / 365)

= USD 1 333 333.33 x 1.0082192

= USD 1 344 292.26

USD 1 344 292.26 sold for ZAR at forward rate

= USD 1 344 292.26 x 7.56114134 = ZAR 10 164 384

ZAR owed to bank after 60 days

= ZAR 10 000 000 x (1 + 0.10 x 60 / 365)

= ZAR 10 000 000 x 1.01643834

= ZAR 10 164 384.

It will be clear that the South African ZAR borrower / USD investor did not benefit from the deal; he is at

break-even. Had he benefited the forward rate would have been out of line, allowing an arbitrage deal to be

undertaken.

From this example it will have been established that if the cost of borrowing is higher than the gain from

lending the forward rate will have to be at a premium to compensate for the interest rate differential. It may

also be explained as follows:

45

If ZAR invested increases by more than USD invested (because of the higher ZAR interest rate), the numerator

(ZAR) will increase by more than the denominator (USD) and thus result in a forward rate that is higher than

the spot rate.

The numerator and denominator referred to are of course from the formula presented above and repeated

here:

Outright forward exchange rate = SP x {[1 + (irvc x t)] / [1 + (irbc x t)]}.

2.10.3 Foreign exchange swaps

Foreign exchange swaps (called Forex swaps or just swaps) are not to be confused with “proper” currency

swaps, which will be covered later. Forex swaps are forward deals done on a different basis, and are the deal

type done by the market maker banks in the vast majority of cases.

A Forex swap is the exchange of two currencies now (i.e. spot) at a specified exchange rate (which does not

have to be the current exchange rate but usually is a rate close to the current rate – it is a benchmark rate on

which the "points" are based) coupled with an agreement to exchange the same two currencies at a

specified future date at the specified exchange rate plus or minus the swap points. Swaps points are also

called forward points and are quoted, for example, as 590 / 600. This quote is interpreted as follows:

the left side (specified exchange rate + 590 points) is the rate at which the quoting bank will buy USD in 60

days for USD sold spot now (client buys spot and sells forward).

the right side (specified exchange rate + 600 points) is the rate at which the quoting bank will sell USD after

60 days for USD bought spot now (client sells spot and buys forward).

It is important to note that the points run from the second decimal and are in terms of price (of the variable

currency). The following should be clear:

Forward swap = outright forward – SP

Outright forward = SP + forward swap

Using the earlier numbers:

Forward swap = outright forward – SP

= 7.5611 – 7.5

= 0.0611

Outright forward = SP + forward swap

= 7.5 + 0.0611

= 7.5611.

46

An example is called for: a number of years ago the South African Reserve Bank encouraged the inflow of

foreign exchange by offering the banks cheap swap rates. This means that the local banks were

“encouraged” to borrow offshore and swap USD for ZAR, which is unwound on the forward date, giving

them a virtually risk-free profit. The following are the numbers (utilising some of the numbers used earlier):

Specified rate (= spot rate = SP) = USD / ZAR 7.5

Period of forward deal = 60 days

Interest rate parity forward rate (i.e. fair value rate) = USD / 7.5611

USD rate (assume borrowing in US) (irbc) = 5.0% pa

ZAR rate (assume lending in SA) (irvc) = 10.0% pa

Forward points offered = 550.

A local bank borrows USD 1 000 000 at 5.0% from a US bank and sells this to the Reserve Bank. The Reserve

Bank credits the bank’s current account in its books (i.e. excess cash reserves) by ZAR 7 500 000 (USD 1 000

000 x 7.5). This of course amounts to the exchange of currencies in the first round of the swap. The Reserve

Bank undertakes to exchange USD 1 000 000 plus interest at 5% for ZAR in 60 days’ time (the second

exchange) at the forward rate of:

Forward rate = specified rate (the benchmark rate) + forward swap points

= 7.50 + 550 (i.e. 0.0550)

= 7.555

Forward consideration (USD) = borrowing x [1 + (irbc x 60/365)]

= USD 1 000 000 x [1 + (0.05 x 60/365)]

= USD 1 000 000 x 1.008219

= USD 1 008 219.

This means that the Reserve Bank will supply USD 1 008 219 at an exchange rate of USD / ZAR 7.555 at the

conclusion of the swap after 60 days.

The bank withdraws the created16 R7 500 000 from the Reserve Bank and invests this in a local bank (other

bank most likely) NCD at 10.0%. The proceeds at the end of the forward period are:

Forward consideration (ZAR) = deposit x [1 + (irvc x 60/365)]

= ZAR 7 500 000 x [1 + (0.10 x 60/365)]

= ZAR 7 500 000 x 1.01643836

= ZAR 7 623 288.

16 Note that this transaction increases bank liquidity (if it is the only transaction that day).

47

On the due date of the swap, the Reserve Bank supplies USD 1 008 219 to the local bank for a ZAR 7 617 095

(USD 1 008 219 x 7.555)17. This amounts to the exchange of currencies in the opposite direction, i.e. it is the

second round of the swap. The local bank fulfils its obligation to the US bank (USD 1 008 219 = borrowing

plus interest), and pockets the profit on the swap of ZAR 6 193. This amount is the difference between the

amount paid by the bank that issued the NCD and the amount paid by the bank to the Reserve Bank in terms

of the swap contract

(ZAR 7 623 288 – ZAR 7 617 095).

2.10.4 Forward-forwards

Figure 2.13: example of a forward-forward deal

30 days

60 days

60 days

Time line

now T+0

Swap = sell USD 30 days forward

and repurchase

USD after 90 days

T+30 T+90T-30

Outright forward to purchase USD after 60 days

Cash flow = + USD (T-30 deal) – USD (T+0 deal)

= 0

Cash flow = + USD (T+0 deal)

A forward-forward is a swap deal between two forward dates as opposed to an outright forward that runs

from a spot to a forward date. An example is to sell USD 30 days forward and buy them back in 90 days time.

The swap is for the 60-day period between 30 days from deal date (now = T+0) and 90 days from deal date.

The backdrop to this deal may be that the client (company) previously bought USD forward (30 days’ ago for

the date 30 days from now) but wishes to defer the transaction by a further 60 days because it will not need

the USD until then. This deal18 is illustrated Figure 2.13.

Variations of forward-forwards are foreign exchange agreements (FXAs) and exchange rate agreements

(ERAs). Together they are referred to as synthetic agreements for forward exchange (SAFEs). The FXA is the

same as a forward-forward as explained above, but on the first settlement date, T+30 in our example, the

settlement takes place as in the case of a FRA, i.e. in cash reflecting the difference between the exchange

rate set in the outright forward contracted on T-30 and the exchange rate set in the swap on T+0.The

difference may be a profit or a loss for the client, which of course will be the reverse for the bank. An ERA is

the same as a FXA, but takes no account of the movement in spot rates between T-30 and T+0.19

17 This transaction decreases bank liquidity

18 Example adapted from Steiner, R (1998: 7-8)

19 See Steiner (1998: 177).

48

2.10.5 Time options

As noted above, when a bank does an outright forward it is undertaking to buy or sell a specified currency on

a future date at an exchange rate specified at the outset. This type of contract does not suit every non-bank

client. A client may have a requirement for a hedge but is not sure exactly when Forex is required (e.g. an

importer), or to be sold (e.g. an exporter). In these cases Forex time options are appropriate instruments.

This instrument is the same as an outright forward with the maturity date specified, but the client has the

option to settle at any time within a specified period. The specified period may be anytime during the period

of the contract, or anytime between a future date and the expiry date of the contract.

A Forex time option is not to be confused with a currency option in terms of which the holder has the option

but not the obligation to buy (call) or sell (put) a specified currency at a specified strike rate before or on the

expiry date. An option premium is payable, which is not the case with a time option. In the case of a time

option, the holder has the obligation to settle but has flexibility in terms of the settlement date.

2.10.6 Functions/uses of the forward foreign exchange market

There are many reasons for the existence of the forward foreign exchange market, but it is essentially used

to cover a number of risks that are encountered by investors and commercial companies that are engaged in

importing and exporting. The four main uses of the forward market are:

• Commercial covering

• Hedging an investment

• Speculation

• Covered interest arbitrage

This is discussed in some detail in the module on the foreign exchange market.

2.10.7 Size of forward foreign exchange market in South Africa

Table 2.2 provides the turnover in foreign exchange forwards in relation to spot and swap transactions for

the years from 1996. The transactions in third currencies numbers include forward transactions (i.e. the split

numbers are not available).

It is to be noted that the numbers are average daily transactions. The average daily turnover in forwards

(swaps and outright forwards) for 2008 was USD 9 560 million. Assuming 12 holidays, the annual turnover in

2008 was USD 2 370 880 million or USD 2.4 trillion. At an exchange rate of USD / ZAR 7.0 this equates to ZAR

16.8 trillion. This gives a good idea of the mammoth size of the market.

49

TABLE 2.2: AVERAGE DAILY TURNOVER IN THE

SOUTH AFRICAN FOREIGN EXCHANGE MARKET (USD MILLIONS)

YEAR

TRANSACTIONS AGAINST THE RAND TRANSACTIONS

IN THIRD CURRENCIES

Spot Swaps Outright

forwards

Total

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

1 503

1 573

1 659

1 309

1 401

1 275

861

769

1 015

1 513

2 021

2 808

3 218

1 274

1 677

3 919

5 624

5 650

5 557

4 697

6 597

6 738

7 703

7 968

8 843

8 695

682

574

750

546

459

475

322

366

414

580

882

904

865

N/A

N/A

1 711

1 995

2 006

2 318

1 943

2 308

3 131

3 506

3 344

3 931

3 670

Source: South African Reserve Bank Quarterly Bulletin. N/A = Not available.

2.11 FORWARDS IN THE COMMODITIES MARKET

Above we have discussed the forward markets in the debt market and the foreign exchange market. There

are also forward markets in many commodities, but they will not be discussed here, because the principle

remains the same. Only the maths is slightly different because other costs, such as storage (which usually

includes insurance), is taken into account:

50

FP = {SP x [1 + (ir x t)]} + (SC x dte)

where

FP = forward price

SP = spot price

ir = interest rate for period, i.e. period from now until the forward deal date

dte = days to expiry (of forward contract, i.e. until forward deal date)

t = dte / 365

SC = storage costs

It will be evident that this is a “carry cost” (CC) model, where there are two costs, interest and storage, and

no income on the asset is forthcoming (if income were forthcoming the model becomes a “net carry cost”

(NCC) model.

Example: forward grain market: one ton of grain will be delivered to a buyer 91 days from today:

SP (of grain) = R1 200 per ton

ir = 12.0% pa

dte = 91

t = 91 / 365

SC = 35 cents per ton per day

FP = {R1 200 x [1 + (0.12 x 91 / 365)]} + (0.35 x 91)

= (R1 200 x 1.0299) + R31.85

= R1 267.75 per ton.

2.12 FORWARDS ON DERIVATIVES

In addition to the forwards that are found in the four financial markets, there are also forwards on swaps.

The specific swaps on which forwards are written are interest rate swaps (IRSs). The forward IRS is an

agreement to enter into a swap at some stage in the future at terms agreed upfront. It differs from a

swaption (discussed later) in terms of which the holder has the right to allow the option to lapse. In the case

of a forward swap, the holder is obliged to undertake the swap at the future agreed date (swaps are

discussed in some detail later).

In South Africa there was one listed forward swap (called a swap forward) and it was listed on BESA (now

part of the JSE) in the past. BESA described the forward swap as follows (minor changes have been effected):

“These are simply standardized forward contracts on underlying swaps which reset against the 3-month

JIBAR. These are traded on the fixed rate of the underlying forward starting swap. They are physically

settled, i.e. with a position in the underlying swap at the fixed rate corresponding to the rate at which the

forward was traded or closed out bilaterally for cash. For each underlying swap there are four swap forward

contracts listed.

51

These have expiries on the first Thursday of February, May, August and November. Contracts are listed on 1-

year, 2-year, 5-year, 7-year and 10-year underlying notional swaps. A fixed for floating swap against the 3

month JIBAR will be delivered as per vanilla swaps. The party with the obligation to pay the fixed rate of the

underlying swap is considered to be long of the contract.”

An example was provided by BESA (small changes have been effected):

“Consider the November 2005 contract that expires on 6 November 2005. It will be quoted as the fixed rate

of the underlying 1-year swap which will start on 6 November 2005 and end on 6 November 2006.

If we assume that the traded rate of the forward is 9% (this will be the fixed rate of the underlying swap at

the forward expiry) traded on any date prior to 6 November 2005, this will become the fixed rate for a SWAP

starting on 6 November 2005 running to 6 November 2006. Therefore, on expiry, if the 3 month JIBAR is 8%

on 6 November 2005, the interest payments for R1 million nominal on 6 Feb 2006 is as follows:

R1 000 000 x 0.09 x 92 / 365 = R22 684.93 on the fixed schedule and

R1 000 000 x 0.08 x 92 / 365 = R20 164.38 on the floating schedule.

A net interest payment of R22 684.93 − R20 164.38 = R2 520.55 will be made to the receiver of the fixed

rate.”

2.13 ORGANISATIONAL STRUCTURE OF FORWARD MARKETS

Figure 2.14 is one way of depicting the organisational structure of the spot financial markets.

However, this applies to the “normal” financial markets, i.e. the money, bond and equity markets. It is not

well suited to the foreign exchange and derivative markets. Figure 2.15 is an attempt to visualise the

derivative markets.

Market nature

PRIMARY MARKET

EXCHANGE

SECONDARY MARKET

Market form

OTC

Market type

Trading driver

Trading system

DERIVATIVE MARKETSSPOT MARKETS

Trading form

ORDER QUOTE

OTC EXCHANGE

PUBLIC ISSUE

PRIVATE PLACEMENT

AUCTION

FLOOR TEL / SCREEN

ATSSCREEN / TEL

SINGLE CAPACITY

DUAL CAPACITY

Issue method

TAP ISSUE

broker AND dealerbroker OR dealer

Figure 2.14: organisational structure of spot financial markets

52

Market nature

PRIMARY MARKET

Market form

Market type

Trading driver

Trading system

DERIVATIVE MARKETS SPOT MARKETS

Trading form

ORDER QUOTE

OTC EXCHANGE

FLOOR TEL / SCREEN

ATSSCREEN / TEL

SINGLE CAPACITY

DUAL CAPACITY

Figure 2.15: organisational structure of derivative financial markets

The derivative markets in the form of the OTC forward markets are entirely primary markets (there are

minor exceptions such as repos that are marketable, but trading in them is rare); thus, generally, one cannot

talk of a secondary OTC derivatives market (in the normal sense of the term). The reason for this situation is

that the forward market instruments are usually custom made for clients. However, this does not mean that

the holder of a forward transaction is “stuck” with the deal until maturity; the instruments are “marketable”

in the sense that the positions created by them may be “closed out” quite easily by the purchase / sale of an

opposite deal. The “closing out” will result a net loss or profit, as in the case of a spot instrument sale.

The same applies in the case of listed (on an exchange) forwards, but with a difference. A secondary market

in these listed instruments also does not exist in the normal sense of the term. However, the contracts are

standardised and can therefore be “closed out” by doing an equal but opposite transaction. In the case of

the OTC forward markets it is not always possible to do the exact opposite transaction, leaving thus a

measure of risk.

This brings us to the trading driver: quote or order. Participants are able to get quotes from the banks or

place an order with a broker-dealer. “Quote” means that the banks provide quotes (as in market making –

explained earlier). This leads to the trading system. In the South African derivative markets, all the trading

systems apply (except “floor”; it does however still apply in some international markets).

53

The trading system “telephone / screen” means applies where broker-dealers quote indication prices on the

screen (for example, the Reuters Monitor System) and clients phone in and ask for firm prices. “Screen /

telephone” is where prices quoted on screen are firm for a certain size deal and the deal is consummated on

the telephone. ATS stands for “automated trading system” and here deals in the form of orders are inputted

into the ATS and are matched by it if there is an opposite order. The various types of forward transactions fit

into one of these three trading systems.

Single and dual capacity trading means that the broker-dealers either act as brokers and dealers (dual) or as

brokers or dealers (single).


Outcomes

• Understand the characteristics of forward markets.

• Understand the essence and mechanics of forward contracts / instruments.

• Understand the mathematics of the forward markets.

• Calculate a forward price.

• Know the advantages and disadvantages of forward markets vis-à-vis futures markets.

• Understand the organisational structure of the forward markets.

Review questions

1. The term 'spot market' refers to derivatives where payments are made in cash. True or false?

2. The motivation for a forward contract is usually that the spot price that will prevail in the future is

uncertain. True or false?

3. A seller who believes that the price of the underlying asset will decline, will enter into a forward contract

to deliver the underlying asset. True or false.

4. The forward price can be calculated using the formula: FP = SP / [1 + (ir – t)]. True or false?

5. In a repurchase agreement the seller of the agreement agrees to resell the security at a later date. True

or false?

6. A 3 x 6 FRA (3-month into 6-month): the 3 in the 3 x 6 refers to 3 months’ time when settlement takes

place, and the 6 to the maturity of the FRA deal, i.e. the rate quoted for the FRA is a 6-month rate at the

time of settlement. True or false?

7. Swaps points are also called forward points and are quoted, for example, as 590 / 600. The left side is the

rate at which the quoting bank will buy ZAR now for USD for resale after 60 days, and the right hand is

the rate at which the quoting bank will sell ZAR now for USD for repurchase after 60 days. True or false?

8. An example of a 60 day forward-forward is to sell USD 60 days forward and buy them back in 90 days

time. True or false?

9. Define a forward market.

10. Define a forward contract.

54

11. What are the main advantages and disadvantages of forward markets?

12. What forward rate should a bank quote a client on R10 million 306-day NCDs delivered to a client in 50

days time; it will have 256 days remaining; the 50-day NCD rate = 5% pa and the 306-day NCD rate = 7%

pa.

13. What will the bank do if a client accepts the quote given in question 12?

14. Define a repurchase agreement.

15. A speculator who believes that bond rates are about to fall (in the next week) buys a 5-year bond to the

value of R5 million at the spot rate of 10.2%. The speculator sells the bond to a broker-dealer for 7 days

at 9.5% pa (the rate for 7-day money). Assume now that the 5-year bond rate falls to 10.1% on day seven

and the bond's value goes up by R50 000. What is the profit or loss of the speculator?

16. R10 million (nominal value) NCDs with a maturity value of R10 985 000, and a market value of R10 500

000, were sold for seven days at a repo rate of 12.5% pa. What would be the interest payable on this

repurchase agreement?

17. Define a forward rate agreement (FRA).

18. The treasurer of a company decides to deal at the 8.20% pa offer rate for the 6 x 9 FRA for an amount of

R20 million, which matches the company’s requirement perfectly. The deal date is 4 June. The benchmark

is the relevant JIBAR rate. On settlement date the benchmark JIBAR rate is 8.60% pa. How much does the

bank that sold the FRA now owe the company?

19. The rate now (spot rate) for 182 days is 9.0% pa and the rate now (spot rate) for 273 days is 10.5% pa,

and we know that the latter rate covers the period of the first rate. What is the implied forward rate?

20. Forward period = 60 days

Spot rate = R6.50 to one US dollar

Relevant interest rate on a dollar investment = 3.0%pa

Relevant interest on a rand investment = 6.0% pa

What is the price of a 60-day forward outright?

55

Answers

1. False. The spot market is also called the “cash market”, and it refers to transactions or deals (which are

contracts) for the delivery of securities that are settled at the earliest opportunity possible.

2. True.

3. True.

4. False. The correct formula is: FP = SP x [1 + (ir x t)].

5. False. In a repurchase agreement the buyer of the agreement agrees to resell the security at a later

date.

6. False. A 3 x 6 FRA (3-month into 6-month): the 3 in the 3 x 6 refers to 3 months’ time when settlement

takes place, and the 6 to the expiry date of the FRA from deal date, i.e. the rate quoted for the FRA is a

3-month rate at the time of settlement.

7. False. The left side is the rate at which the quoting bank will buy back USD in 60 days for USD sold now,

and the right hand is the rate at which the quoting bank will sell USD in 60 days for USD bought now.

8. An example of a 60-day forward-forward is to sell USD 30 days forward and buy them back in 90 days

time. It could also be to sell USD 60 days forward and buy them back in 120 days time.

9. A forward market is a market (essentially a primary market) where a deal on an asset is concluded now

for settlement at a date in the future at a price / rate determined now.

10. A forward is a contract between a buyer and a seller that obliges the seller to deliver, and the buyer to

accept delivery of, an agreed quantity and quality of an asset at a specified price (now) on a stipulated

date in the future.

11. The main advantages that can be identified for forward markets are:

• Flexibility with regard to delivery dates


The main disadvantages are:

• The transaction rests on the integrity of the two parties, i.e. there is a risk of non-performance

• Both parties are “locked in” to the deal for the duration of the transaction, i.e. they cannot

reverse their exposures

• Delivery of the underlying asset takes, i.e. there is no option of settling in cash

• The quality of the asset may vary

• Transaction costs are high.

12. Slightly lower than the 7.34% pa break-even IFR in order to make a small profit.

13. As soon as this deal is consummated, the banker will immediately purchase R10 million 306-day NCDs at

the 306-day rate of 7.0% pa in order to hedge itself (and to make the profit).

14. A repurchase agreement (repo) is a contractual transaction in terms of which an existing security is sold

at its market value (or higher) at an agreed rate of interest, coupled with an agreement to repurchase

the same security on a specified, or unspecified, date.

56

15. R40 890.41 [= 50 000 – (5 000 000 x 7/365 x 0.095)]

16. R25 171.23 [= 10 500 000 x 0.125 x 7/365]

17. A forward rate agreement (FRA) is an agreement that enables a user to hedge itself against

unfavourable movements in interest rates by fixing a rate on a notional amount that is (usually) of the

same size and term as its exposure that starts sometime in the future.

18. R19 545.62 {= (20 000 000 x 0.004 x 91/365) x [1/(1 + (0.082 x 91/365))]}

19. 12.92% {= {[1 + (0.105 x 273/365)] / [1 + (0.09 x 182/365)] –1} x 365/91}

20. R6.53 to the dollar {= 6.50 x [1 + (0.06 x 60/365)] / [1 + (0.03 x 60/365)]}

2.15 USEFUL ACTIVITIES

Forward products listed on Yield-X:

http://www.yield-x.co.za/products/product_specifications/index.aspx

Forward products listed on BESA:

http://www.bondexchange.co.za/besa/action/media/downloadFile?media_fileid=2887

Bond calculator: http://calculator.bondexchange.co.za/

57

CHAPTER 3: FUTURES




Chapter 2 Forwards

Chapter 3 Futures

Chapter 4 Swaps

Chapter 5 Options




• Define a futures contract.

• Understand the constituents of the definition of futures contracts.

• Understand the payoff (risk) profile of futures contracts.

• Understand the characteristics of the futures market, such as getting out of a position in

futures, and cash settlement versus physical settlement.

• Understand the concepts of margins, marking to market and open interest.

• Comprehend the principles applied in the pricing of futures contracts (fair value).

• Calculate the fair value prices of futures contracts.

• Understand the concepts of convergence, basis and net carry cost in relation to basis.

• Understand the motivation for undertaking deals in futures, particularly hedging, and the

participants in the futures market.

3.3 INTRODUCTION

In the previous chapter on forwards, we defined a forward market as a market where a transaction (buy or

sell) on an asset is concluded now (at T+0) for settlement on a date in the future at a price determined now. A

forward contract may therefore be defined as a contract between a buyer and a seller at time T+0 to buy or

sell a specified asset on a future date at a price set at time T+0. We also identified the advantages and

disadvantages of forward markets. We also covered variations on this main theme, such as FRAs, FIRCs and

repos.

Essentially, futures contracts are standardised forward contracts, and they developed because forward

contracts have some disadvantages, the most obvious one being that forward contracts do not easily offer

the advantage of reversing transactions.

58

There is also a need for efficient price discovery which means that liquidity needs to be enhanced, and this

only comes about when activity in the market increases, and for this contracts need to be standardised in

terms of quality, quantity and expiry date. Once this need is satisfied an exchange is an appropriate market

form, and an exchange mitigates risk, which further enhances the breadth and depth of the market.

This does not mean that all forward markets are destined to become futures markets. In some markets

reversibility of deals is not crucial and customisation in terms of quantity and expiry is required. The best

example is the outright forward Forex market where commercial transactions (importing and exporting)

require customisation and rarely require reversal.

Futures are discussed in the following sections of this chapter:

• Futures defined

• An example

• Trading price versus spot price

• Types of futures contracts

• Organisation of futures markets

• Clearing house

• Margining and mark to market

• Open interest

• Cash settlement versus physical settlement

• Payoff with futures (risk profile)

• Pricing of futures (fair value versus trading price)

• Fair value pricing of specific futures

• Basis and net carry cost

• Participants in the futures market

• Hedging with futures

• South African futures market contracts

• Risk management by SAFEX

• Mechanics of dealing in futures

• Size of futures market in South Africa

• Economic significance of futures market

3.4 FUTURES DEFINED

3.4.1 Introduction

A futures contract may be defined as a contractual obligation in terms of which one party undertakes at T+0

to sell an asset at a future time and price (determined at T+0) and the other party undertakes to buy the

same asset on the same future date at the same price. This sounds pretty similar to the forward contract. It

is, but the differences are that the contracts are standardised, the underlying assets are standardised, and

the contracts are exchange-traded, because these qualities render the contracts marketable (sort of – later

we will see that futures are marketable in the sense that they can be “closed out” by undertaking an equal

and opposite transaction).

59

As noted, essentially the futures markets of the world developed to overcome the disadvantages of forward

markets. By their very nature, forward markets are OTC markets (mostly), whereas futures markets are all

formalised in the form of financial exchanges, the members of which effect all trading, and the exchange

guarantees all transactions by interposing itself between buyer and seller.

The definition of a future may now be extended: a standardised contract which obligates the buyer to accept

delivery of, and the seller to deliver, a standardised quantity and quality of an asset at a pre-specified price

on a pre-stipulated date in the future.

It may be useful to break up this definition into its constituents:

• Standardised contract between two parties.

• Buyer and seller.

• Delivery.

• Standardised quantity.

• Standardised quality.

• Asset.

• Price.

• Expiry date.

• Market price.

3.4.2 Standardised contract between two parties

All futures contracts in all international futures markets are standardised. The future is a legal contract

between two parties setting out the details. At least one party to the contract must be a member of the

exchange. As noted, even though a client may buy a future from, or sell a future to, a member of the

exchange, the transaction is guaranteed by the exchange, i.e. the exchange acts as the seller for each buyer,

and as the buyer for each seller. In this way it interposes itself in each futures deal. This may be illustrated

(simply) as in Figure 3.1.

BUYER OF FUTURE

SELLER OF FUTURE

Contract FUTURES EXCHANGE

Contract

Figure 3.1: participants in futures deal

3.4.3 Buyer and seller

It should be evident that the futures market is a typical example of a “zero sum game”, i.e. for every buyer of

a contract there is a seller. Consequently, if the buyer makes a loss, the seller gains by the same amount. The

converse is obviously also true. As noted earlier, the buyer and the seller deal with a member of the

exchange, unless the buyer and seller are members of the exchange.

60

3.4.4 Delivery

Even though the standard definition of a future emphasises delivery, in practice this is rare, particularly in

the financial futures markets. The reason for this is simply that the participants in the futures markets prefer

settlement of the profit or loss on expiry date. Even if they wanted delivery, in many cases this is not

possible. In the case of a future on an equity index, for example, it is impossible to deliver the index.

Nowadays, delivery takes place in only a few financial and commodity futures contracts.

3.4.5 Standardised quantity

Every futures contract obviously has a specific size (as opposed to a forward contract where size is

negotiated between buyer and seller). For example, in the case of the equity index futures contracts in South

Africa, the size of each contract is R10 x the index value. In the commodities futures markets the contract

sizes are usually multiples of standard units, for example, barrels, bushels, etc.

3.4.6 Standardised quality

This is important in the commodities futures markets, particularly in the case of perishable assets. Quality is

obviously not an issue in the case of financial futures markets. In these markets contracts are based on a

specific underlying asset or notional asset the quality of which does not vary.

3.4.7 Asset

A futures contract is a derivative instrument, i.e. it and its value are derived from an underlying asset and it

cannot exist in the absence of this asset. The underlying assets of futures contracts can be divided into two

broad categories, i.e. specific assets and notional assets, and there are various subcategories under each,

such as storable assets, perishable assets, income-producing assets, etc.

Specific (also called “physical”) assets include specific bonds, pork bellies, etc, while notional assets include

indices and interest rates, for example the FTSE/JSE Top 40 Index, the FTSE/JSE ALTX 15 Index, the FTSE/JSE

FINI 15 Index, etc. One may also categorise futures broadly into financial futures and commodity futures,

and then split them further into sub-categories as follows:

Financial futures:

• Interest rates (for example, future on a specific bond, future on a bond index).

• Equities (for example, future on an individual share, future on equity index).

• Currencies (for example, future on the USD/ZAR exchange rate, future on currency index).

Commodity futures:

• Agricultural (for example, future on livestock, future on maize).

• Metals and energy (for example, future on gold price, future on crude oil).

61

3.4.8 Price

Price is the core of a future. Essentially, futures market participants are fixing a price now for settlement in

the future. Clearly therefore, the price of the future is related to the price of the underlying instrument. As

the price of the underlying instrument varies, so does the price of the future (but not always to the same

extent).

3.4.9 Expiry date

The other vital feature of futures contracts is the expiry date, i.e. the date when delivery or cash settlement

takes place. Needless to say, the price of the future at the expiry time on the expiry date is equivalent to the

spot price. It will therefore be clear that the futures price moves closer to the spot price as time goes by (i.e.

it converges on the spot price).

3.4.10 Market price

The contract trades (i.e. can be bought or sold or reversed = “closed out”) because it has a value, and this

value is largely influenced by the spot price of the underlying asset, but also by expectations. Price is the only

feature of the future that varies. Each contract has a minimum movement size or “tick size”, for example R1.

3.5 AN EXAMPLE

The above definitional section may be rendered more meaningful if an example of a futures transaction is

introduced at this stage (see Box 3.1for a futures deal transaction advice).

BOX 3.1: EXAMPLE OF FUTURES DEAL (TRANSACTION ADVICE OF BROKER)

THB

Truly Honest Brokers (Pty) Limited

Member of Financial Derivatives Division of JSE - SAFEX

55 Dorp Street

Stellenbosch 7600

TRANSACTION ADVICE

Mr. RIP van Winkel

1025 Dork Street

Stellenbosch

8600

Date produced: 10 March 2005

Time produced: 14:35

Page: 1/1

Account number: 001

Deal

date

Deal ref

no

Dealt

by

Deal

type

Time

dealt

Your

deal

No

dealt

Price /

premium*

SAFEX

DRN

Deal costs

Commis-

sions

Booking

fee

10/3/05

10/3/05

005714

005718

THB

THB

Agency

Agency

12:22

15:40

Mar 05

ALSI

Buy

Sell

10

10

16577

16564

Matched

Matched

0.00

0.00

(22.00)

(22.00)

0.00 R (44.00)

* Premium applies to options on futures. This is a standard confirmation / transaction advice.

62

In this example (which is an actual example that took place in the past20) the member of the exchange (i.e.

the broker) is THB, and the client (i.e. the person who did the deal) is a Mr. RIP van Winkel.

The relevant future is the “March 2005 ALSI”, the full name of which is the FTSE/JSE All Share Index future,

which expired at 12 noon on 15 March 2005. The deal was done on 10 March 2005 at 12:22 pm and the

client bought the future at a price of 16577. This price of 16577 is the “trading” price, i.e. the price at which

the trade (deal) took place. As noted earlier, for every buyer there is a seller, i.e. the price of 16577 is the

price at which a willing buyer and a willing seller were prepared to deal.

It will be understood that the trading price differs from the spot price, i.e. the current price of the underlying

asset. The underlying asset, as noted, is the FTSE/JSE ALSI Index (which is updated continuously by the JSE).

At the time of the trade (12:22 pm), the index value could have been 16523, for example.

The client would have bought the particular future either to hold until expiry date (15 March 2005) or for

short-term speculative reasons. In the former case the expiry price was the index value at 12:00 on 15 March

2005. This was recorded at (an assumed) 16617 (which of course were not known on 10 March). Thus, had

the client held the future until expiry, she would have profited (and the seller lost) - see below. As can be

seen from the transaction advice (Box 3.1), however, the client “closed out her position”, i.e. did the

opposite transaction (sold the future) at 15:40 on the same day. She did this transaction at the then

prevailing price for the future, i.e. 16564.

What was the financial position of the client at 15:40 pm on 10 March 2005? The value of the contract (as

set down by the exchange) is R10 times the trading price. We also know that the client bought and sold 10

contracts. The client’s financial position is shown in Table 3.1.

TABLE 3.1: FINANCIAL POSITION ON CLOSEOUT

Price Contract value Number of contracts Total value (exposure)

Purchase leg 16577 R165 770 10 R1 657 700

Sale leg 16564 R165 640 10 R1 656 400

Difference (loss) R1 300

Dealing costs R 44

Total loss R1 344

Because the client bought the future (i.e. bought the index), she was clearly hoping that the index (and the

trading price) would rise. Instead, the trading price decreased, and she made a loss.

20 Names and other details, such as price (index) level have been changed.

63

TABLE 3.2: FINANCIAL POSITION ON CLOSEOUT

Price Contract value Number of contracts Total value (exposure)

Purchase leg 16577 R165 770 10 R1 657 700

Expiry 16617 R166 170 10 R1 661 700

Difference (profit) R4 000

Dealing costs R44

Total profit R3 956

If the client had held the contract until expiry, when the index was recorded at (an assumed) 16617, she

would have profited as shown in Table 3.2.

It is a feature of futures markets that no money changes hands when a deal is struck. However, both buyer

and seller are required to make a “good faith” deposit - termed the “margin” (note: this was the origin of the

margin, but it is now part of the risk management procedures of the exchange). This deposit is made with

the broker who, in turn, passes it on to the exchange.

BOX 3.2: TRANSACTION ADVICE OF EXCHANGE - PURCHASE

FINANCIAL DERIVATIVES DIVISION OF JSE - SAFEX

TRANSACTION ADVICE

The following contract has been accepted by SAFEX

SAFEX acceptance number: 04032818

You have: BOUGHT Number of contracts: 10

Type: MARCH 2005 ALSI PRICE / YIELD: 16577

Date of deal: 10 MARCH 2005 Time dealt: 12.22

Broker: THB (Agent)

Dealer: John Broke

This had the effect of: Opening 10 LONG Positions

Closing Positions

Attention: Mr. RIP van Winkel, 1025 Dork Street, Stellenbosch, 8600

64

BOX 3.3: TRANSACTION ADVICE OF EXCHANGE - SALE

FINANCIAL DERIVATIVES DIVISION OF JSE - SAFEX

TRANSACTION ADVICE

The following contract has been accepted by SAFEX

SAFEX acceptance number: 04032818

You have: SOLD Number of contracts: 10

Type: MARCH 2005 ALSI PRICE / YIELD: 16564

Date of deal: 10 MARCH 2005 Time dealt: 15:40

Broker: THB (Agent)

Dealer: John Broke

This had the effect of: Opening Positions

Closing 10 LONG Positions

Attention: Mr. RIP van Winkel, 1025 Dork Street, Stellenbosch, 8600

In conclusion, it is important to again point out that the exchange interposes itself between buyer and seller

and guarantees the transaction. Effectively thus, clients are dealing with the exchange. All transactions are

also confirmed by the exchange (see Box 3.2 and Box 3.3).

3.6 FUTURES TRADING PRICE VERSUS SPOT PRICE

It should be clear at this stage that buyers and sellers of futures contracts trade at the market prices for the

relevant futures, i.e. at the prices established in the market by the interplay of supply and demand. It is also

apparent that these prices are different from the prices of the underlying assets, but that the prices of

futures are closely related to the prices of the underlying assets. An example is required.

The example in the Figure 3.2 depicts the life of a three-month future created on 31 March and expiring on

30 June. It will be evident that the buyer of the future on 31 March who holds it to expiry on 30 June profits

(and the seller loses of course). She bought the future at 110 when the spot price was 100 and it “closed

out” at 132. Similarly, the buyer of the future on 30 April at 122 (when the spot price was 112) also profits,

but to a lesser extent. The buyer of the future on 31 May at 138 (when the spot price was 124), however,

makes a loss because the futures price declined to 132 on expiry date (= spot price).

As noted earlier, the price of a future always converges upon the spot (cash market) price. The reason is that

the so-called basis (which is similar to net carry cost – see below) becomes smaller with the passage of time.

On expiry date the basis (and net carry cost) is zero.

65

Loss

Prof it

Price /

index

100

140

130

120

110

31/3 30/4 31/5 30/6

Prof it

Period to expiry

132

122

112

124

138

Futures price

Index value (spot price)

Figure 3.2: example of a 3-month future (index)

It can be seen that the future traded above the spot price for the entire life of the contract. This is not

always the case, however. At times the future can trade at a discount to the spot price. Also clear from the

above is that the difference between the two prices is not consistent. This is because expectations at times

play a major role in the determination of the futures price.

13500

14000

14500

15000

15500

16000

16500

03-Mar May Jul Sep Nov 04-Jan Mar May Jul Sep Nov 05-Jan Mar

Ind

ex

Figure 3.3: March 2005 ALSI future

Index (spot value of ALSI)

Market price of future (MTM)

66

TABLE 3.3: MARCH 2005 ALL SHARE INDEX FUTURES CONTRACT

Year Month Value of index

(spot rate)

Market rate (price / value) of

future (mark to market)

2003 March 13535 13665

April 13733 13860

May 13992 14120

June 14054 14223

July 14177 14525

August 14011 14282

September 13792 14030

October 13916 14252

November 14183 14425

December 14889 15415

2004 January 14754 15262

February 14846 15235

March 14939 15185

April 15357 15870

May 15396 15865

June 15404 15515

July 15651 15865

August 15833 15948

September 15676 15712

October 15724 15862

November 15756 15840

2005 December 15860 15965

January 15054 15165

February 15147 15173

March (15th) 15277 15277

Two examples may be useful (the numbers are from the Table 3.3):

A buyer of 10 contracts (one contract = R10 x market price) of the March 2005 ALSI on 30 April 2003 would

have “bought” an exposure in the equity market (ALSI) to the value of R1 386 000 (10 x R10 x 13860). If this

position were held until “close out”, i.e. 15 March 2005, the buyer would have profited to the extent of R141

700 [R1 527 700 (10 x R10 x 15277) – R1 386 000]. The seller of the contract would of course have lost this

amount (if she held the contract until expiry).

A buyer of the 10 contracts on 30 July 2004 would have bought exposure to the ALSI of R1 586 500 (10 x R10

x 15865). If she held the future until expiry, she would have made a loss R58 800 [R1 527 700 (10 x R10 x

15277) – R1 586 500].

67

3.7 TYPES OF FUTURES CONTRACTS

There are many futures exchanges around the world, and the variety of contracts is vast. Table 3.4 shows an

excerpt of the contracts that are listed (from Wall Street Journal).

There are various contracts under each of these names, i.e. contracts that have different expiry dates. For

example, there may be four S&P 40 contracts running simultaneously – the 15 March, the 16 June, the 15

September, and the 15 December.

TABLE 3.4: EXAMPLES OF FUTURES CONTRACTS

FINANCIAL COMMODITIES

Interest rate Equity Foreign currencies Agricultural Metals and energy

Physical

Treasury bonds

Treasury notes

Treasury bills

Federal funds

Canadian govt bond

Eurodollar

Euromark

Euroyen

Eurobond

Index (notional)

Short sterling bond

index

Long sterling bond

index

Municipal bond

index

Physical

Various specific

shares

Index (notional)

DJ Industrial

S&P 500

NASDAQ 100

CAC-40

DAX-30

FTSE 100

Toronto 35

Nikkei 225

NYSE

Physical

Japanese yen

DM

British pound

Swiss franc

French franc

Australian dollar

Brazilian real

Mexican peso

Sterling/mark cross

rate

Index (notional)

US dollar index

Grains and oilseeds

Wheat

Soybeans

Corn (maize)

Livestock and meat

Cattle – live

Hogs – lean

Pork bellies

Food and fiber

Cocoa

Coffee

Sugar

Cotton

Orange juice

Physical - Metals

Gold

Platinum

Silver

Copper

Aluminium

Palladium

Physical - Energy

Crude oil – light

sweet

Natural gas

Brent crude

Propane

Index (notional)

CRB index

Physical = the actual instrument, currency, commodity. Index = indices of exchanges, etc. CRB index =

Commodity Research Bureau.

It is to be noted that The Wall Street Journal’s futures contract complete list is about three times the above

list provided. In South Africa, the futures market is only about 16 years in the making. Consequently, the

number of futures listed is relatively small; a selection is shown in Table 3.5.

68

TABLE 3.5: SELECTION OF SOUTH AFRICAN FUTURES CONTRACTS



Physical

Futures on:

R186 long bond

(10.5% 2026)

R194 long bond

(10.0% 2008)

R201 long bond

(8.75% 2014)

3-month JIBAR

interest rate

Notional swaps (j-

Notes)

FRAs (j-FRAs)

Index (notional)

Futures on:

ALBI index (j-ALBI)

GOVI index(j-GOVI)

Physical

Futures on:

+ / - 200 shares

(called single

stock futures –

SSFs)

Dividends (local &

foreign)

Index (notional)

Futures on:

FTSE/JSE Top 40

FTSE/JSE INDI 25

FTSE/JSE FINI 15

FTSE/JSE FNDI 30

FTSE/JSE RESI 20

FTSE/JSE African

banks

FTSE/JSE gold

mining

Physical

USD/ZAR

EUR/ZAR

GBP/ZAR

AU/ZAR

Index (notional)

None

Physical

Local:

White maize

Yellow maize

Soybeans

Wheat

Sunflower seed

Foreign (underlying =

foreign futures)

Corn

Index (notional)

None

Physical

Local:

Kruger Rand

Foreign (underlying =

foreign futures)

Gold

Platinum

Crude oil

Index (notional)

None

3.8 ORGANISATIONAL STRUCTURE OF FUTURES MARKETS

Financial markets have many aspects to them. One way of depicting the organisational structure of financial

markets is as in Figure 3.4.

Does the futures market have both primary markets and secondary markets? The answer is that the market

type is primary market; however, while futures cannot be sold, they can be “closed out” at any time by

dealing in the opposite direction. The “closing out” results a loss or profit as in the case of a spot instrument

sale (or purchase in the case of a “short” sale21) in the secondary market.

21 “Short” sale means the sale of an instrument that the seller does not own. The seller borrows the instrument from an investor /

lender for a fee and delivers it back to the lender when the short sale is unwound by the purchase of the instrument. A short sale is

undertaken to profit opportunistically from an expected decline in price.

69

Market nature

PRIMARY MARKET

Market form

Market type

Trading driver

Trading system


Trading form

ORDER QUOTE

OTC EXCHANGE

FLOOR TEL / SCREEN

ATSSCREEN / TEL

SINGLE CAPACITY

DUAL CAPACITY


The market form of the futures market is formal in the shape of an exchange. There are many futures

exchanges in the world or futures divisions of exchanges as in the case of South Africa.

As regards trading driver and the trading system, the futures market in South Africa is order and ATS

(automated trading system), i.e. an order-matching method on an ATS is followed. This requires some

elucidation:

The broking members of the exchange register their clients with the exchange. This is in fact unique in that

most futures exchanges do not know who the clients of the members are.

The members we refer to by the generic term broker-dealers, because they may deal as principals or agents

and the capacity of trading is disclosed to the client. The broker-dealers at times deal in dual capacity in a

single deal (see last bullet point).

Some broker-dealers do not have clients and only deal as principals, and some broker-dealers deal only as

agents with clients (both are called single capacity).

The ATS is constructed in such a way that broker-dealers input their orders into the system (directly onto a

computer). An example is buy 300 December ALSI contracts at 9020 (this is an index value). Sellers do so

also. The system places on the screen the best buy and sell orders for all the different contracts, and has a

drop-down facility where the non-best buy and sell orders appear (to show the depth of the market).

Because the buyers and sellers are ultimately to deal with the exchange, the identities of the broker-dealers

are not displayed.

70

When two opposite orders match, the deal is automatically consummated by the ATS, and the two members

are informed via the system. The clients (if applicable) are informed in turn by their broker-dealers.

A broker-dealer, as noted, can deal in dual capacity, meaning that a single order can be split between

principal and agent. For example, the buy example mentioned earlier can be 100 contracts as principal and

200 contracts as agent.

Because large deals (defined as for example over 500 contracts) may affect prices unduly, the rules of the

exchange allow for off-ATS trading. These deals are negotiated between members and then reported on the

ATS. However, most futures deals are done via the ATS.

The above is the organisation of the South African futures market. In some futures markets, the open outcry

floor method of trading is preferred. This is also an order driven trading system, which is highly transparent

because the broker-dealers face each other in a “trading pit”, i.e. ensuring that clients’ orders (and broker-

dealer’s own orders) are transacted at the best prices. An ATS may be seen as imitating the transparency of

floor trading.

As regards delivery, in the futures markets delivery of the underlying asset usually does not take place. This

is discussed in the later section “cash settlement versus physical settlement”. However, unlike as in the case

of forwards (the unsophisticated future) margin is required. This is discussed after the following section on

clearing.

3.9 CLEARING HOUSE

All deals are cleared through a clearing house that is usually separate from the exchange. The clearing house

may be regarded as being responsible for the management of the market. The clearing house in the South

African futures market is Safex Clearing Company (Pty) Limited (SAFCOM).

We noted earlier that as soon as a deal is struck, the exchange (SAFCOM) interposes itself between the two

principals that concluded the deal. This means that it takes on the opposite side of each leg of each deal.

SAFCOM is backed by a Fidelity fund.

3.10 MARGINING AND MARKING TO MARKET

The exchange requires that for each transaction the client is obliged to place with it a “good faith deposit’,

which is called the margin deposit. At the start of a deal this is called the initial margin, and this is set by the

exchange (see contracts below). It is usually 5-8% of the value of the contract22. The initial margin may be

defined as a deposit required on futures deals that will ensure that the obligations under the contracts will be

fulfilled.

22 Note that the percentage differs from exchange to exchange and from contract to contract. With some contracts the initial

margin is calculated on the basis of the riskiness (measured as standard deviation) of the contract. For example, Yield-X in a

December 2007 Market Notice (Y128) stated: "After consultation with the Clearing Banks the JSE has recalculated all the IMRs using

a revised statistical methodology which takes into account 3.5 standard deviations as opposed to the 6 standard deviations

previously used. The revised IMR percentages for all contracts will change monthly depending on the movement in the underlying

spot market, but the 3.5 standard deviation remains constant."

71

The initial margin essentially protects the exchange from default because it is extremely unlikely that losses

on positions will exceed the initial margin. At the end of each day the margin account is topped up, where

required (i.e. in the case of losses). Each contact is marked to market every day, meaning that at a point in

time each contract is “valued”. This takes place at the end of the trading day and it is based on the last

settlement price.

The purpose of the marking to market is to ensure that the margin account is kept funded. If the mark to

market price is lower that the purchase price, i.e. if the holder of a future is making a loss, she has to top up

the margin account to the proportionate level it was. This amount is called the variation margin. If a holder

makes a profit, a credit to the margin account is made. The ultimate purpose is to ensure that the exchange,

which has taken on the risk of guaranteeing the trades, is protected.

From this it follows that if a holder of a future makes a loss and is unable to top up the margin account, the

exchange will “close the member out”. This means that the exchange takes an offsetting contract. The loss in

then deducted from the client’s margin account balance, and he is paid out.

3.11 OPEN INTEREST

A term that often crops up in the futures market is “open interest”. This is the term for the number of

outstanding contracts of a particular contract, i.e. the number of contracts that are still open and obligated

to delivery (physical or cash settlement). Double counting is avoided in the number. If broker-dealer A takes

a position in a future and B takes the opposite position, open interest is equal to 1. Open interest on a

particular contract may be depicted as in Figure 3.5 (daily from start of contract to its expiry date).

When a contract is launched by an exchange, open interest is zero. As participants begin to trade, open

interest rises, and this continues until the maturity date approaches. On maturity date the future is “closed

out” and open interest is again zero (because the contract is replaced with another that has a new maturity

date).

Openinterest

Contract expires

Contractstarts

Time

Figure 3.5: open interest

72

3.12 CASH SETTLEMENT VERSUS PHYSICAL SETTLEMENT

In many of the commodities markets physical settlement takes place. This means that the commodities that

underlie futures contracts are delivered at expiry of the contract. In the financial futures markets, physical

delivery also takes place in some cases (for example, certain of the bond contracts), but in the majority of

cases settlement takes place in the form of cash settlement.

Many traders in futures markets where delivery is required resort to trade reversing prior to expiry of the

contract, and the reason for doing so is that they do not want to deliver or receive the physical goods/metals

etc. These traders are involved in the market for speculative or hedging reasons, and take an opposite

position to the one they hold prior to maturity, in so doing liquidate their position at the clearing house.

3.13 PAYOFF WITH FUTURES (RISK PROFILE)

The gains and losses on futures are symmetrical around the difference between the spot price on expiry of

the futures contract and the futures price at which the contract was purchased. A simple example may be

useful (see Figure 3.6): one futures contract = one share of ABC Corporation Limited.

On the vertical axis we have the profit or loss scale of the future. On the horizontal axis we have the price of

the future at expiry (= spot price). If the long future is bought at R70 and the price at expiry is R71, the profit

is R1, i.e. for each R1 increase in the price of the future, the profit is R1. Thus, if the spot price on maturity is

R90, the profit is R20 (R90 – R70).

Figure 3.6: payoff with long futures contract (risk profile)

(SPm)spot price on maturity (expiry) of contractR50

PP

Prof it on long futures contract

Loss on long futures contract

R70 R90

-R20

+R20

R110R30

-R40

+R40

73

PP

Prof it

on short

futures contract

Loss on short

futures

contract

R70 R90

-R20

+R20

R110R30 R50

-R40

+R40

(SPm)spot price on

maturity (expiry) of contract

Figure 3.7: payoff with short futures contract (risk profile)

It will be apparent that if the spot price on maturity is SPm, and the purchase price is PP, then the payoff on a

long position per one unit of the asset is:

SPm – PP.

It follows that the payoff in the case of a short future (see Figure 3.7) is:

PP – SPm.

It will also be clear that the payoff on a future is a total payoff because nothing was paid for the contract

(remember the margin is a deposit that earns interest and is repayable in full).

3.14 PRICING OF FUTURES (FAIR VALUE VERSUS TRADING PRICE)

The reader should at this stage already have a good idea of the principle involved in the pricing of futures

contracts. Some elaboration, however, will be useful. All or some of the following factors influences the

theoretical price of a future, which is also termed the fair value price:

• Current (or “spot”) price of the underlying asset.

• Financing (interest) costs involved.

• Cash flows (income) generated by the underlying asset.

• Other costs such as storage costs and insurance premiums.

74

The theoretical price of a future is equal to the spot price (SP) of the underlying asset, plus cost-of-carry or

carry cost [financing cost (usually the risk free rate23 is used here) plus other costs (OC) such as insurance

and storage] (CC) less any income earned (I) (CC – I = net carry cost, NCC) expressed as a proportion of the

SP. This may be written as follows (t = remaining term of contract in days / 365):

Fair value price (FVP) = SP + {SP x [(CC - I) x t]}

= SP + [SP x (NCC x t)]

= SP x [1 + (NCC x t)].

An example may be handy (OC = 0 here because the example uses an index future).

The table and graph shown earlier (Table 3.3 and Figure 3.5) are expanded to include the fair value (or

theoretical) prices at the end of each month24 (see Table 3.6 and Figure 3.8). Taking April 2004 as an

example, we have the following:

Spot price (SP) = 15357

CC = risk free rate (rfr) (assumed) = 8.0% pa

I = assumed dividend yield = 2.0% pa

t = term to maturity of contract / 365 = 319 / 365

FVP = SP x [1 + (NCC x t)]

= SP x {1 + [(rfr – I) x t]}

= 15357 x {1 + [(0.08 – 0.02) x (319 / 365)]}

= 15357 x [1 + (0.06 x 0.873973)]

= 15357 x 1.052438

= 16162.

As can be seen from Table 3.6, even though the theoretical price was 16162, the March 2005 future traded

at 15870 at the end of April 2004, i.e. at a discount to the theoretical price.

23 In most derivative formulae the risk free rate (rfr) is used, and this is so because it is a well known and easily accessible rate. There

is no standard definition for the rfr but most analysts / academics apply this term to the 91-day treasury bill rate.

24 Prices are of course available minute to minute and the mark to market price is set once a day.

75

TABLE 3.6: MARCH 1995 ALL SHARE INDEX FUTURES CONTRACT

Year Month Value of index

(spot rate)

Market rate

(price / value) of

future (mark to

market)

Fair value price

2003 March 13535 13665 15124

April 13733 13860 15277

May 13992 14120 15494

June 14054 14223 15493

July 14177 14525 15557

August 14011 14282 15303

September 13792 14030 14996

October 13916 14252 15060

November 14183 14425 15279

December 14889 15415 15963

2004 January 14754 15262 15744

February 14846 15235 15773

March 14939 15185 15796

April 15357 15870 16162

May 15396 15865 16125

June 15404 15515 16057

July 15651 15865 16235

August 15833 15948 16343

September 15676 15712 16104

October 15724 15862 16073

November 15756 15840 16028

2005 December 15860 15965 16053

January 15054 15165 15160

February 15147 15173 15184

March (15th) 15277 15277 15277

It will be apparent that the above made use of simple interest. In the case of compound interest, the formula

changes to:

FVP = SP x (1 + NCC)t.

Using the above example:

FVP = SP x (1 + NCC)t

= 15357 x 1.060.87397

= 15357 x 1.052244

= 16159.

It is clear that compounding makes little difference in the case of short-term contracts.

76

13500

14000

14500

15000

15500

16000

16500

03-Mar May Jul Sep Nov 04-Jan Mar May Jul Sep Nov 05-Jan Mar

Inde

x

Figure 3.8: March 2005 ALSI future

Index (spot value of ALSI)

Market price of future (MTM)

Fair value price of future

3.15 FAIR VALUE PRICING OF SPECIFIC FUTURES

In the previous section we covered the basic principle (formula) for valuing futures. However, there are a

number of variations on the theme, because there are different types of futures contract traded.

The (valuation) mathematics pertaining to the different futures is illustrated with the following futures:

• Short-term interest rate futures.

• Individual bond futures.

• Equity index futures.

• Individual equity futures.

• Commodity futures.

• Currency futures.

• Futures on other derivatives

• Other futures.

3.15.1 Short-term interest rate futures

In the case of short-term interest rate futures, the theoretical price or fair value price (FVP) is determined

from the calculated forward-forward rate (which is also called the implied forward rate). An example is

required here: the South African 3-month JIBAR, the specifications of which are shown in Table 3.725.

25 It is to be noted that the 3-month JIBAR future was discontinued in 2004 because of lack of interest. It has not been replaced. For

this reason, and because similar interest rate futures trade in foreign markets, we retain the 3-month JIBAR future as an example.

77

TABLE 3.7: SPECIFICATIONS OF THE 3-MONTH JIBAR FUTURE

CODE JIBAR

UNDERLYING INSTRUMENT The 3-month Johannesburg Interbank Agreed Rate (JIBAR)

CONTRACT SIZE R1 000 000 nominal

EXPIRY DATES & TIMES 11h00 on third Wednesday of the contract month (or previous business

day)

QUOTATIONS 100 minus the yield

MINIMUM PRICE MOVEMENT 0.01 [Tic value = R1 000 000 x (0.01 / 100) x 3/12 = R25]

EXPIRY VALUATION METHOD

Based on the 3-month JIBAR rate as quoted on Reuters page SAFEY.

The settlement price is 100 minus the JIBAR rounded to three decimal

places

Source: Safex (2005).

The first step is to determine the implied forward rate and the second step is to deduct this rate from 100.

Step 1

day1

1month

3months

6months

Time line

implied rate = 11.74% pa

7.0% pa 9.0% pa 10.5% pa8.0% pa

Spot rates

Figure 3.9: JIBAR spot rates and implied rate

Shown in Figure 3.9 are the JIBAR rates quoted on the day a client wishes to buy a 3-month JIBAR futures

contract (i.e. a 3-month rate in 3 months' time).

The rate now (spot rate) for three months is 9.0% pa and the rate now (spot rate) for six months is 10.5% pa,

and the period of the latter rate covers the period of the first rate. The rate of interest for the three-month

period beyond the first three-month period can be calculated by knowing the two spot rates mentioned. This

is called the forward rate of interest, or the implied forward rate, or the forward-forward rate. This is

calculated as follows (assumption 3-month period = 91 days; 6-month period = 182 days):

78


where

IFR = implied forward rate

irL = spot interest rate for 6-month (i.e. long) period

irS = spot interest rate for 3-month (i.e. short) period

tL = 6-month (i.e. long) period, expressed as number of days / 365 (= 182 / 365)

tS = 3-month (i.e. short) period, expressed as number of days / 365 (= 91 / 365)

IFR = {[1 + (0.105 x 182/365)] / [1 + (0.09 x 91/365)] –1} x [365 / (182 – 91)]

= [(1.05235616 / 1.02243836) –1] x (365 / 91)

= 0.02926123 x 4.010989

= 0.11736647

= 11.736647% pa.

This derived interest rate may be tested as follows: if R1 million (present value, PV) is placed on deposit for 6

months at the abovementioned 6-month rate of 10.5% pa, the future value (FV6-m) amount would be:

FV6-m = PV x [1 + (0.105 x 182 / 365)]

= R1 000 000 x 1.05235616

= R1 052 356.16.

Alternatively, if an investment were made for 3 months, the following would be the total:

FV3-m = PV x [1 + (0.09 x 91 / 365)]

= R1 000 000 x 1.02243836

= R1 022 438.36.

If this amount (R1 022 438.36) is invested for 3 months at the implied forward rate of 11.736647%, the FV6-m:

FV6-m = PV x [1 + (0.11736647 x 91 / 365)]

= R1 022 438.36 x 1.02926123

= R1 052 356.16.

As expected, this number is identical to the FV of the six-month investment calculated above.

Step 2

The implied forward rate is 11.736647% pa. Internationally, short-term interest rate futures contracts (the 3-

month JIBAR futures in South Africa) are quoted on an index basis, and the index is equal to 100 minus the

annualised rate of interest. Therefore the fair value price (FVP) of the interest rate future in our example is:

79

FVP = 100 – IFR

= 100 – 11.7366

= 88.2633528.

The fair value of the contract (remember contract size = R1 000 000) in our example is R882 633.53 (R1 000

000 x 0.882633528). Keep in mind that the fair value is not necessarily equal to the market value (= mark to

market value as determined by the exchange), and that the difference between the index value at the start

of the contract and the index value at termination thereof is settled at R25 per “tick”, i.e. 0.01 [R1 000 000 x

(0.01 / 100) x (3 / 12) = R25]. This will become clearer in the section on hedging.

It will be apparent that the forward-forward pricing of futures (although they are 100 minus the annualised

rate) is the same as the pricing of an FRA. An FRA can thus be seen as the OTC26 equivalent of the interest

rate future. This calculation also applies to the forward-forward foreign exchange swap.

3.15.2 Individual bond futures27

The principle that underlies the fair value price of a bond future is the NCC [carry cost (rfr) less income] as

discussed. However, the calculation is more elaborate because of the existence of coupon payments, clean

and dirty (all-in) prices, ex and cum interest and so on. The fair value price (FVP) of an individual bond future

is made up of:

Investment (all-in) price + carry cost – income.

An example is required: R157 bond future:

Bond = R157

Maturity date = 15 September 2015

Coupon (c) =13.5% pa

Coupon payment dates (cd1 and cd2) =15 March and 15 September

Yield to maturity (ytm) = 8.2%

Carry cost (CC) (= rfr) = 7.5% pa

Purchase (valuation) date of future (fvd) = 20 June

Termination date of future (ftd) = 31 August28

Books (register) closes = one month before coupon dates29.

26 However, note that in South Africa there is also an exchange listed FRA (on Yield-X, a division of the JSE). In most countries FRAs

are OTC instruments.

27 The author acknowledges the assistance of Alan Joffe and Colin Wakefield in respect of this section.

28 Assumed for purposes of the example; in practise futures terminate in the middle of relevant months.

29 We assume this for purposes of the example (spacing in the illustration); in practice the books close 10 days before the coupon

dates.

80

As noted, the FVP of a bond future is made up of three parts:

FVP = A + B – C (investment + carry cost – income30

)

where

A = dirty (all-in) price of underlying bond at market (current) rate on bond futures valuation date (fvd)

31

= 105.71077 (note: this price is assumed so that it does not date)

B = carry cost factor (i.e. future value factor)

= A x {(rfr / 100) x [(ftd – fvd) / 365]}

= 105.71077 x [0.075 x (72 / 365)]

= 105.71077 x (0.075 x 0.19726)

= 105.71077 x 0.014795

= 1.56394

C = (c / 2) x (1 + {(rfr / 100) x [(ftd – cd2) / 365)]})

[if the futures termination date crosses a books closed date and its associated coupon date (i.e.

is not ex-interest)]

or

= (c / 2) / (1 + {(rfr / 100) x [(cd2 – ftd) / 365)])

[if the futures termination date crosses a books closed date but not the associated coupon date (i.e.

is in ex-interest period, which is the case here)]

= (13.5 / 2) / (1 + {0.075 x [(cd2 – ftd) / 365]})

= 6.75 / {1 + [0.075 x (15 / 365)]}

= 6.75 / [1 + (0.075 x 0.04110)]

= 6.75 / 1.00308

= 6.72927.

Thus:

30 “Income” is too simple a description; it should be described as "accumulated value of income received during the life of the

futures contract" (suggested by Colin Wakefield).

31 Another assumption made is that bond transactions are settled on deal date (so that the example is rendered uncomplicated). In

practice bond deals are settled on T+3. Thus, in the example, the fvd and the ftd should be regarded as settlement dates.

81

FVP = A + B – C

= 105.71077 + 1.56394 – 6.72927

= 100.5454.

Figure 3.10: example of individual bond future

time line

72 days

Jun

coupon date

coupon = 13.5%

Jul OctMay

20 June

NovApr

coupon date

coupon = 13.5%

15 Mar

15 Aug

register closes

f tdfvd cd2

31 Aug

SepMar

15 Sep

15 days

AugFeb

cd1

3.15.3 Equity index futures

We covered the case of equity index futures in our first example where the simple interest net carry cost

calculation was introduced:


= SP x {1 + [(rfr – I) x t]}.

Here we provide another example (All Share Index - ALSI - future):

SP (i.e. index value) = 10765

rfr = 11.5% pa

I (dividend yield, assumed) = 3.5% pa

t (number of days to expiry of contract / 365) = 245 / 365


= SP x {1 + [(rfr – I) x t]}

= 10765 x {1 + [(0.115 – 0.035) x (245 / 365)]}

= 10765 x (1 + (0.08 x 0.6712329))

= 10765 x 1.05369863

= 11343.

82

3.15.4 Individual equity futures

Individual equity / share futures are also called single stock futures (in short SSFs). Calculation of the FVP of

SSFs is the same as above – i.e. as for equity index futures, except that the dividend yield will be easier to

predict.

The JSE also offers an increasing array of SSFs on internationally listed shares (the underlying). Examples are

Apply, Nokia, BP, bank of America, Berkshire Hathaway, Vodafone and Coca-Cola. They are termed IDXs in

short by the JSE.

It is appropriate to mention a futures product which is closely allied with SSFs: the dividend future (DIVF).

They are used to hedge against the dividend risk that accompanies a position in a SSF. As we have seen,

dividend expectations (I) are part of the FVP calculation; therefore there is a need for such contracts.

3.15.5 Commodity futures

In the case of commodity futures, the simple interest net carry cost calculation is also applicable. Although

we have discussed it before, another example will do no harm. The future is the Kruger Rand gold coin future

that has 90 days to expiry, and the size of the contract is equal to the gold price in rand. We assume the

following:

SP = R2881.15

rfr = 7.5% pa

I = 0 (there is no income on a gold coin)

t = 90 / 365.

The fair value price is:


= SP x {1 + [(rfr – I) x t]}

= 2881.15 x {1 + [(0.075 – 0) x (90 / 365)]}

= 2881.15 x {1 + [0.075 x (90 / 365)]}

= 2881.15 x [1 + (0.075 x 0.246575)]

= 2881.15 x 1.018493

= R2934.43.

With commodities where insurance and storage is payable (such as maize), and the amount is not

proportional to the spot price, it is simply added to the FVP.

83

3.15.6 Currency futures

Currency futures are similar to foreign exchange forward contracts, and the covered interest parity formula is

therefore applicable:

FVP = SR x {[1 + (irvc x t)] / [1 + (irbc x t)]}

SR = spot rate

irvc = interest rate of variable currency for period to expiry

irbc = interest rate for base currency for period to expiry

t = number of days to expiry of contract / 365.

An example is called for [base currency (i.e. the 1 unit currency) = GBP; variable currency = USD]:

SR = GBP / USD 1.5

irvc = 5.5%

irbc = 8.5% pa

t = 182 / 365

FVP = SR x {[1 + (irvc x t)] / [1 + (irbc x t)]}

= USD 1.5 x {[1 + (0.055 x 182 / 365)] / [1 + (0.085 x 182 / 365)]}

= USD 1.5 x (1.027425 / 1.042384)

= USD 1.5 x 0.985649

= USD 1.47847.

It will be evident here that the formula is similar to the net carry cost (NCC) one, with the difference being

that there are two rates of interest taken into account: the foreign rate and the local rate.

3.15.7 Futures on other derivatives

As in the case of forwards (forwards on swaps) there are futures on other derivatives. There are two such

examples in South Africa: futures on FRAs (called j-FRAs), and futures on swaps (called j-Notes). Both are

listed on Yield-X (a division of the JSE).

3.15.8 Other futures

Another future listed on the JSE deserves mention: the variance future (VARF). Variance is a statistical

measure of volatility (= risk). The generally accepted measure of risk in the Finance discipline is the standard

deviation of an asset’s return (= the extent of deviation from the mean return). Standard deviation is closely

related; it is the square root of variance.

The variances and standard deviations of returns on assets (like shares) change considerably from time to

time. It is also a major input in the pricing of options. There is a need by some investors to hedge against this

risk, and certain speculators seek exposure to this risk. These two parties make the trading of this instrument

a possibility.

84

In short, a variance future is a futures contract on realised annualised variance of returns on assets / indices.

This instrument is regarded by some as a new asset class.

3.16 BASIS AND NET CARRY COST

Participants in the futures market frequently use the jargon “basis”, “net carry cost” and “convergence”. As

time goes by, the futures price (FP) and the fair value price (FVP) converges on the spot price (SP), and they

are equal on the expiry date of the future.

Futures expiry date

Price

FVPFP

Time

Convergence

SP

NCC

B

Figure 3.11: basis, net carry cost and convergence

Net carry cost (NCC) is the difference between the theoretical or fair value price (FVP) and the spot price (SP)

of the underlying asset:

NCC = FVP – SP.

This is simply because, as we saw:

FVP = SP + NCC.

Basis (B), on the other hand, is the difference between the FP and the SP of the underlying asset:

B = FP – SP.

The NCC and the B may be illustrated as in Figure 3.11.

85

It will be apparent that the FVP is higher than the SP when the NCC is positive [i.e. when the carry cost (CC) is

higher than the income (I) on the underlying asset]. However, when I > CC, i.e. NCC is negative, the FVP < SP.

When NCC is negative, the FP is usually also negative. In this case it is market practice to quote the basis in a

positive manner as:

B = SP – FP.

3.17 PARTICIPANTS IN THE FUTURES MARKET

3.17.1 Introduction

The participants in the futures market can be categorised in a number of ways. One can, for example,

categorise participants according to membership of Safex in which case one would have two categories:

members and non-members. One could further split members into clearing members and non-clearing

members, and members may also be split into broking members and non-broking members. Each category is

touched upon below.

3.17.2 Clearing members

According to the Rules of Safex, clearing members are those that32:

• Have own funds of at least R200 000 000, or any other sum determined by the Executive Committee

from time to time.

• Maintain and keep in force a surety ship in favour of the clearing house by a financial institution.

• Enter into a clearing house agreement with the exchange.

• See to the settlement of proprietary trading and client trading and those deals conducted by non-

clearing members for whom it clears.

3.17.3 Non-clearing members

According to the Rules of Safex33, a non-clearing member:

• Who does not receive a client’s margins or hold the clients margins shall have an initial capital of

R200 000 or thirteen weeks operating costs, whichever is greater or such other minimum amount

that the Executive Committee may determine.

• Who receives clients’ margins or holds clients’ margins shall have an initial capital of at least R400

000 or thirteen weeks operating costs whichever is greater or such other minimum amount that the

Executive Committee may determine.

• Settles all trades with their clearing member.

32 See www.safex.co.za

33 See safex.co.za

86

3.17.4 Broking members

In terms of the rules of Safex34, a broking member:

• May deal for own account and/or for non-members (i.e. clients).

• May be a clearing member or a non-clearing member.

• Shall not be a natural person.

• Shall have the systems and expertise to administer their own and client funds in accordance with the

derivative rules of the JSE.

• Shall have adequate capital as set out above, per the derivative rules of the JSE.

3.17.5 Non-broking members

The rules determine that a non-broking member:

• May only deal for their own account (i.e. they may not deal for clients).

• May be a clearing member or a non-clearing member.

• Shall not be entitled to trade with clients or enter into any client agreements.

• Shall have adequate capital as set out in the derivative rules of the JSE.

3.17.6 Non-members

Non-members are obviously all the participants in the market that are not involved in broking / dealing for

others and that are obliged to effect all futures transactions through broking members. One could classify

non-members in various ways such as:

• Foreign sector.

• Household sector (individuals).

• Corporate sector.

• Financial intermediaries:

o Banks.

o Insurers.

o Pension funds.

o Collective investment schemes (CISs).

3.17.7 Summary

In summary we have:

Members:

• Clearing members:

o Broking members (deal for own account and/or for non-members).

o Non-broking members (deal only for own account.

• Non-clearing members:

o Broking members (deal for own account and/or for non-members).

o Non-broking members (deal only for own account)

Non-members (deal only with members).

34 See safex.co.za

87

3.17.8 Functionality

One could also classify participants in the futures market according to functionality as follows:

• Investors.

• Arbitrageurs.

• Hedgers.

• Speculators.

These participants are found in both the categories non-members and members of the exchange, meaning

that some members themselves are engaged in investing, arbitrage, hedging and speculation. All the

participants in the futures market may be depicted as in Figure 3.12.

Non-members

Deal for own account

MEMBERS OF SAFEX

Non-clearing

members

Broking members

Non-broking members

Deal for clients

Settle all trades with

their clearing member

Clearing

members

Figure 3.12: participants in the futures market

INVESTORS / HEDGERS / ARBITRAGEURS / SPECULATORS

Investors

Investors in the futures market are those participants that view the futures market as an alternative to the

cash market (i.e. the underlying market). For example, an investor may wish to earn the All Share Index

(ALSI) and, instead of buying the shares in the proportions that make up the index, can achieve this by

buying the appropriate number of ALSI futures contracts. She may do this for the sake of convenience, to

avoid transactions costs (depending on the fair value price) or she may view the underlying market as lacking

in liquidity.

88

An investor may also use long-term instruments and short futures contracts to invest short-term, or use

short-term financial instruments and long futures contracts to invest long term.35 These positions are

alternatives to straightforward investing for the desired investment horizon (see Table 3.8).

TABLE 3.8: USE OF FUTURES TO MANAGE THE INVESTMENT HORIZON

Investment

term desired

Cash market

alternative Use of futures market alternative What is known? Comparison

3 months

(March to June)

Buy 3-month

treasury bill (in

March; maturity

June)

• Buy government bond with 10-year

maturity

• Sell (go short of) a 10-year

government bond futures contract

with June maturity

• Buy rate

• Sell rate locked

in

Compare

computed rate

with 3-month

treasury bill rate

10 years

(it is now March)

Buy 10-year

government

bond

(in March)

• Buy (go long of) a 10-year

government bond contract with

June maturity

• Invest funds in 3-month treasury

bill (March – June)

• Buy rate

locked in

• 3-month rate

locked in

Arbitrageurs

Arbitrageurs endeavour to profit from price differentials (mispricing) that may exist in different markets on

similar securities. For example, if the INDI futures price is trading far in excess of its fair value price, the

arbitrageur may sell the future and buy the equities that make up the industrial index.

Arbitrageurs play a significant role in the futures market by ensuring that futures prices do not stray too far

from fair value prices and by adding to the liquidity of the market.

Hedgers

Hedgers are those participants that have exposures in cash markets and wish to reduce risk by taking the

opposite positions in the futures markets. Most investors, such as pension funds, life offices and banks

hedge their portfolios from time to time in the financial futures market. The equivalents in the commodity

futures markets are the producers and consumers of commodities.

The opposite parties to hedgers are usually the speculators that willingly take on risk in order to profit from

their views in respect of the future movement of prices / rates. Thus, hedgers transfer risk to speculators.

Speculators

Speculators are those participants that endeavour to gain from price movements in the futures market.

Given the small outlay (i.e. the margin) in comparison with cash markets (where the full price is paid),

speculators are attracted to futures markets because they are able to “gear up”.

35 In this regard see McInish (2000: 334).

89

For example, if a speculator has R1 million with which to speculate, she is able to buy shares to the value of

R1 million in the cash market. In the futures market she is able to get exposure (and risk) to the extent of the

amount on hand times the reciprocal of the margin requirement. Thus, if the margin requirement is 8% of

the value of the future/s, she is able to go long of futures by 12.5 (1 / 0.08) times R1 million.36

Speculators and hedgers play a significant role in the futures market in terms of enhancing the liquidity of

this market. It should be apparent that hedgers endeavour to eliminate or reduce risk faced from holding

inventories of financial instruments or commodities, while speculators assume the risk. Thus, speculators

willingly take on the risks transferred to them by hedgers.

It will be evident that there is no clear-cut distinction between membership of the exchange and

functionality. For example, an arbitrageur may be a member of the exchange. Similarly, a speculator may be

a member of the exchange, and he may be a broking or a non-broking member. Broking members can

generally be divided into 3 categories, i.e. those dealing for own account (i.e. arbitrageurs and/or

speculators) (in which case they may be non-broking members), pure brokers and those dealing for own

account and for clients. Note that it is one of the significant rules of the exchange that if a broking member

takes the opposite position of a client, she is obliged to inform the client as such.

One may also categorise participants in the exchange into local and foreign participants. There are a number

of foreign members of Safex. The members of Safex can be found at www.safex.co.za.

Closing remark

Because of the significant role played by hedgers in the futures market, the function of hedging is covered

further in some detail in the following section.

3.18 HEDGING WITH FUTURES

3.18.1 Introduction

Hedging may be defined as the transferring of risk from the hedger, who has a portfolio or who is awaiting a

certain sum of cash, to some other party in the market, usually another hedger or speculator. The hedger is

concerned with price movements that may influence her existing portfolio, or a planned or anticipated

portfolio.

The opportunities for hedging are many, and many a book has been written on hedging strategies. As this is

an introductory text, this section deals with hedging basics and jargon and provides a few hedging examples.

3.18.2 Hedging basics and jargon

The jargon for hedging operations is interesting. For example, the investment community uses the terms

micro hedging and macro hedging37. Micro hedging is where each item in a balance sheet (liabilities and/or

assets) is valued separately and an autonomous hedge set up for each item.

36 It is this property of the futures market, and the significant losses made by some irresponsible traders, that gives the futures

market a bad name.

37 In this regard see Falkena (1989: 39-59).

90

Macro hedging is where the aggregate asset and/or liability portfolios are considered, and the overall risk is

hedged in one operation. Examples are interest rate gap management (a banking problem) and changing

asset allocation (an institutional problem).

A hedger may have a certain hedging horizon, i.e. a certain date on which the hedge will end (for example, a

maize farmer who wishes to hedge from the planting stage to the harvest stage), or have no horizon at all

(for example, a maize dealer who holds a permanent portfolio of maize and supplies feedlots and millers as

they demand the product).

A hedge may be a long hedge or a short hedge, and they may be anticipatory hedges or cash hedges. A

hedge may also be a direct hedge or a cross hedge. For example, a manufacturer of bread requires wheat on

a regular basis. If the manufacturer requires additional wheat in two months’ time and is concerned that the

price will rise over this period, it is able to put in place a long anticipatory hedge by buying an appropriate

number of wheat contracts now that mature in two months’ time (if it is happy with the two-month futures

price). This action fixes the delivery price in two months’ time.

A short hedge is where the hedger sells a futures contract. For example, a gold producer is concerned that

the gold price will fall sharply over the next three months when it will have 5 000 ounces to market, which

will adversely affect profitability. Assuming that the producer is pleased with the three-month delivery

futures price, it will sell an appropriate number of gold contracts (assuming no physical delivery) and thereby

fix its price of delivery. If the spot price in three months time is lower than the futures price it will sell the 5

000 ounces at the spot price; but it will profit on the futures contracts to the extent of the difference

between the spot price and the futures price. Thus, the producer’s delivery price will be the futures price.

Generally, it is difficult to exactly match the cash market position with the futures hedge position

undertaken, in terms of:

• Time horizon.

• Amount of the asset / commodity.

• Characteristics of the goods (e.g. maize or wheat grade).

In these cases the hedger will attempt to match as closely as possible the characteristics of the cash market

asset with the futures position; the hedge will be a cross hedge.

Hedgers wish to establish a hedge ratio (HR). This ratio establishes the number of futures contracts to buy /

sell for a given position in the cash market. The hedge ratio is given by:

HR = - (futures position / cash market position).

The hedger will undertake HR units of the futures to establish the futures market hedge. For example, if HR =

-1, the hedger will have a matched long cash position and a short futures position.

A few examples of hedging follow.38

38 With some assistance from Pilbeam, 1998.

91

3.18.3 Hedging using the 3-month JIBAR future

We assume that it is 20 June 2005 and the 3-month JIBAR future expires on 19 September 2005. We further

assume that Company A has a loan of R1 million at an interest rate of 3-month JIBAR + 2% (on 20 June JIBAR

= 11%, i.e. the borrowing rate is 11% + 2% = 13%), and it is reprised on the JIBAR future expiry dates (which

are the third Thursday of March, June, September and December).

Thus, the borrowing rate now (20 June 2005) for 3 months is 13%, and is due to change again on 19

September (obviously, it is unknown today). The company is concerned that the 3-month JIBAR rate on 19

September will be higher and the company will therefore pay a higher rate for the 3-month period following

19 September.

The company hedges itself by selling a 3-month JIBAR futures contract (contract size is R1 million). The price

now is 89, reflecting the current 11% 3-month JIBAR rate. During the course of the next three months the

price of the contract will move up or down in minimum amounts of 0.001 (“minimum price movement” –

see the contract specifications in Table 3.12), also called “tick size”, which equates to R2.50 [(91 / 365) x

(0.001 / 100) x R1 000 000].

If the company is correct in its view (increasing rates) and the future closes out at 88 on 19 September (i.e. a

new 3-month rate of 12% pa), the company makes a profit of R2 493.15 [1 00039 x (91 / 365) x (0.001 / 100)

x 1 000 000]40 on the futures contract. This amount is offset against the new rate it will be paying on its

borrowing for the next three months, i.e. 14% (12% + 2%). It will be evident that the “extra” the company

will be paying (14% - 13%) in the next 3-month period is R2 493.15 [(1.0 / 100) x (91 / 365) x R1 000 000].

The two amounts are identical.

TABLE 3.9: HEDGING WITH INTEREST RATE FUTURE

Date / rate Cash market position Problem Solution

• 20 June

• 3-month JIBAR

rate = 11% pa

• Borrowing of

R1 000 000

• Rate = JIBAR + 200bp

• Reprising every 91

days

• Borrowing rate = 11% + 2% =

13%

• Concerned that rates will rise

and borrowing rate will increase

on next reprising date of 21

September

• Sell R1 000 000 3-month

JIBAR future (maturity 21

September)

• Price 89.0 (100 – 11%)

• 19 September

• 3-month JIBAR

rate = 12% pa

Roll over borrowing at

new rate = 12% + 2%

• No problem. Expectation that

rates will be unchanged at next

reprising date

• Future closes out at 88.0

(100 – 12%)

• Profit = 1 000 x (91/365) x

(0.001 / 100) x R1 000 000 =

R2 493.15

• Result: borrowing rate of

13% locked in

Tick size = 0.001 (in price) = R2.50

39 One percentage point / 0.001 (ie 1 / 0.001).

40 This formula may also be written simply as [(91 / 365) x (1 / 100) x 1 000 000]. The “1” in “1 / 100” refers to the 1% (ie 100bp or 1

000 “ticks”) change in the price of the future (purchase price to closeout price).

92

It will also be apparent that a speculator, who does not have a cash market “position”, and who undertook

the above futures position, would have benefited to the extent of R2 493.15. Had rates declined by 100bp

over the period, she would have lost this amount, i.e. the correct futures position would have been a long

contract in the case of falling rates.

3.18.4 Hedging with share index futures

TABLE 3.10: HEDGING WITH SHARE INDEX FUTURE

Date / price Cash market

position Problem Solution

• 28 June

• ALSI = 9000

• 19 September

ALSI future

price = 9150

• Share portfolio of

R92 000 well spread

over share market

(representative of

share market)

• Concerned that share

prices will fall over next

few months and that

portfolio will be worth

less

• Sell September ALSI future at

current price of 9150 (maturity 19

September)

• Contract size = 10 x index value = 10

x 9150 = exposure of R91 500

• 19 September

• ALSI = 8513

• Share portfolio

value = R85 755

• No problem

• Expectation that share

prices will move sideways

• Future closes out at 8513

• Profit = 91 500 – 85 130 = R6 370

• Total portfolio value R85 755 in

shares + R6 370 in cash = R92 125

An individual has a portfolio valued at R92 000 that is well spread over the share market. The all share index

currently (28 June 2005) is 9000, and the September all share index future (September ALSI, due 19

September) is trading at 9150. The individual is concerned that share prices “across the board” are about to

fall sharply, and that the value of her portfolio will fall commensurately.

The individual decides to sell the September ALSI future. The contract size is 10 times index value, i.e. R91

500 (10 x 9150). She sells the ALSI future, and it closes out at 8513 on 19 September. The profit made is R6

370.00 [R91 500 – R85 130 (8513 x 10)].

She compares this with the loss in the market value of the portfolio of R6 245 (R92 000 - R85 755.0041). This

loss is more than compensated for by the profit on the futures position of R6 370.00.

41 An assumed number.

93

3.18.5 Hedging with currency futures

A South African exporter is convinced that the USD proceeds (assume USD 100 000) from a export order will

be worth less when it is received in three months time, as a result of the dollar depreciating (the rand

appreciating). The exporter sells a rand/dollar futures contract (contract size USD 100 000) at USD / ZAR 10.2

which happens to be the same as the spot rate42. It has three months to expiry. The value of the contract

now in rand terms is R1 020 000.

At the end of the three month period, i.e. when the contract expires, the rand/dollar exchange rate is USD /

ZAR 9.55. The contract (which is settled in cash) value on expiry is R955 000. The exporter makes a profit of

R65 000 (R1 020 000 – R955 000) on the futures contract.

TABLE 3.11: HEDGING WITH CURRENCY FUTURE

Date / price Cash market

position Problem Solution

• Now

• Spot rate =

USD / ZAR

10.2

• Futures price

= USD / ZAR

10.2

• Exporter

expecting USD

100 000 in 3

months time

• Concerned that USD will

depreciate (ZAR appreciate)

• Sell rand/dollar 3-month future at

USD / ZAR 10.2

• Contract size = USD 100 000

• Contract value = R1 020

000 (USD 100 000 x 10.2)

• Three months

later

• Spot rate =

USD / ZAR

9.55

• Sell proceeds of

USD 100 000

at spot rate =

R955 000

• Exporter earned

R65 000 less

• No problem

• Expectation that exchange

rates will move sideways

• Therefore no need to hedge

next USD proceeds of export

transaction

• Future closes out at USD / ZAR

9.55

• Contract value = R955 000 (USD

100 000 x 9.55)

• Profit = R1 020 000 – R955 000 =

R65 000

The export proceeds of USD 100 000 are received, which is converted at the new rand/dollar spot rate of

USD / ZAR 9.55, i.e. a rand value of R955 000. On this leg the exporter “loses” R65 000 (meaning earns this

amount less). Through hedging (short anticipatory hedge) the exporter “locked in” a certain outcome. Of

course she gave up a potential gain (if the USD / ZAR exchange rate depreciated to say USD / ZAR 11.0) in

exchange for a certain outcome. This is the price of hedging.

42 Because USD and ZAR interest rates are the same (assumed).

94

3.19 SOUTH AFRICAN FUTURES MARKET CONTRACTS

A selection of JSE-listed futures contracts, and their specifications,43 is as shown in Table 3.12 [excluding the

individual share futures contracts (single stock futures - SSFs), the specifications of which are shown in Table

3.13].

There are close to 200 SSFs listed on the JSE. Their specifications are identical (except for the futures codes)

are shown in Table 3.13.44

TABLE 3.12: JSE CONTRACTS AND SPECIFICATIONS

FUTURES

CONTRACT

FTSE/JSE TOP

40 INDEX

FUTURE

FTSE/JSE GOLD

MINING INDEX

FUTURE

FTSE/JSE

SA LISTED

PROPERTY

INDEX

KRUGER RAND

FUTURE BOND FUTURES

CODE ALSI GLDX SAPI KGRD VARIOUS

UNDERLYING

INSTRUMENT

FTSE/JSE Top 40

Index

FTSE/JSE Gold

Mining Index

Future

FTSE/JSE SA

Listed Property

Index

Kruger Rand

Various listed

bonds – e.g.

R201, R203

CONTRACT

SIZE

R10 x Index

Level

R10 x Index

Level

R10 x Index

Level 1 Kruger Rand

R100 000

nominal

EXPIRY DATES

& TIMES

15h40 on 3rd

Thursday of

Mar, Jun, Sep &

Dec. (or

previous

business day if a

public holiday)

13h40 on 3rd

Thursday of

Mar, Jun, Sep &

Dec. (or

previous

business day if a

public holiday)

13h40 on 3rd

Thursday of

Mar, Jun, Sep &

Dec. (or

previous

business day if a

public holiday))

17h00 on 3rd

Thursday of

Mar, Jun, Sep &

Dec. (or

previous

business day if a

public holiday)

12h00 on the

first business

Thursday of

February, may,

August &

November

QUOTATIONS Index Level (no

decimal points)

Index Level (no

decimal points)

Index Level to

Two Decimal

points

In whole Rands

to 2 decimals

Ytm (generally

nacs) for

settlement on

the delivery

date

MINIMUM

PRICE

MOVEMENT

One Index Point

(R10)

One Index Point

(R10) 0.01 0.01 1/10th point

SETTLEMENT

METHOD Cash Settled Cash Settled Cash Settled

Physically

settled

Delivery of the

physical bond

43 Almost verbatim from www.safex.co.za. All the futures and their specifications can be found on this website.

44 Verbatim from www.safex.co.za.

95

TABLE 3.13: INDIVIDUAL SHARE FUTURES CONTRACTS LISTED ON THE JSE

FUTURES CODE Various

UNDERLYING

INSTRUMENT The various listed companies

CONTRACT SIZE 100 x the share price (e.g. share price 85.25, future price R8,525.00)

110 x the share price for NEDQ

EXPIRY DATES & TIMES

If the contract is a constituent of any of the traded indices, 15h40 on the 3rd

Thursday of Mar, Jun, Sep & Dec. (Or the previous business day if a public holiday)

If the contract is not a constituent of any of the traded indices, 17h00 on the 3rd

Thursday of Mar, Jun, Sep & Dec. (Or the previous business day if a public holiday)

QUOTATIONS Price per underlying share to two decimals

MINIMUM PRICE

MOVEMENT R 1 (R 0.01 in the share price)

EXPIRY VALUATION

METHOD

If the contract forms a constituent of any of the traded indices then, arithmetic

average of 100 iterations taken every 60 seconds between 14h01 and 15h40 will

be used. If the contract does not form a constituent of any of the traded indices

then, the official closing price determined by the JSE Securities Exchange will be

used

SETTLEMENT METHOD Physically settled in terms of Rule 8.4.7.

3.20 RISK MANAGEMENT BY SAFEX

Safex itself states boldly that its risk management philosophy “… is very simple – ‘You stand good for your

client.’ What this means is that each member will carry its client’s losses if the client defaults just as each

clearing member will carry its member’s (for whom it clears) losses if the member defaults. This pyramid

structure forms the basis of the Safex Risk Management Structure.” The structure is depicted as in Figure

3.13.

JSE / SAFEX

SAFCOM

CLEARING

MEMBER

CLEARING

MEMBER

MEMBER MEMBER MEMBER MEMBER

CLIENT CLIENT CLIENT CLIENT CLIENT CLIENT CLIENT CLIENT

Figure 3.13: risk management by Safex

96

The responsibility of appropriate risk management is placed on the shoulders of the clearing members who,

in turn, pass this accountability onto the members for whom they clear, i.e. the non-clearing members. They,

in turn, risk manage in terms of the rules of the exchange which stipulates the “levying” of a margin deposit.

As noted, Safex requires a margin deposit to be paid by all participants when they take on a position in

futures. This margin is registered in the name of the client or member, and it is equivalent to between 2%

and 8% of the value of the contract. This is a reflection of the parameters of the risk that is associated with

trading in the futures market in one day. As noted earlier, the initial margin is reassessed each day by Safex

and brings into play the variation margin.

Ultimately, the risk that Safex bears is the risk that one of the clearing members defaults, whether the result

of a non-clearing member causing it to default or as a result of its own activities. However, this is remote, as

the clearing members of Safex are all major banks.

3.21 MECHANICS OF DEALING IN FUTURES45

NOTE FOR SAIFM RPE EXAM STUDENTS:

THIS SECTION (3.21) WILL NOT BE EXAMINED

Participation in the futures market is only possible through a broker-dealer who is a member of SAFEX. A

client wishing to conduct a futures transaction would contact his broker by telephone. A typical conversation

between client and broker would begin with a “rundown” of current market conditions including:

• Current market prices.

• Recent movements in prices.

• Market bid, offered or range trading.

• Other market influences such as:

o world market movements

o gold, silver, platinum prices

o currency prices and movements

o bond market trends

o political news and events

o economic indicators released recently.

• Current local orders or expected orders in the market, i.e. the existence of sizeable deals which

could affect the direction of the market.

• Foreign participation in the market (foreign organizations’ usually deal in large volumes which has a

major influence on prices).

• Option volatilities (bid and offered).

• Option strike prices, and puts and calls traded recently - i.e. indicators of market sentiment.

• Technical indicators, etc.

45 This section draws heavily on the past broking experience of portfolio manager JPM (Philip) Faure.

97

The prices of financial instruments are the outcome of available information and the transactions based on

available information. The above, therefore, is simply part of the information dissemination process. The

depth of information provided varies from client to client depending on the client’s experience and

involvement in the market. A client who is knowledgeable on the market and who actively trades is usually

confident of his ability and would generally phone his broker and place an order. A less active client would

ask the broker for a “rundown” of the market and what the broker would do if he were the client. This type

of client would usually terminate the conversation and digest the information before phoning back with an

order.

The client will ask the broker to buy or sell a certain quantity (number) of contracts of a specific future for a

certain expiry date. A price limit is usually stipulated. If the broker is not able to execute the transaction

within the stipulated limit, he will refer back to the client for further instructions (and give the reasons for

not being able to execute). The price limit agreed upon with the client is influenced by many factors

including:

• Where the market is trading (bid, offer).

• Liquidity of market (volume trading, i.e. activity).

• Whether the market is well bid or well offered.

• Width of the bid-offer spread, etc.

The broker is obliged to do the trade at the best price for the client and as quickly as possible. In this regard

it will be evident that:

In the case of a buying order: if the market is well bid (termed a “bid market”) it is difficult to put a bid in and

get one’s price.

In the case of a selling order: if the market is well offered (termed an “offered market”) it is not easy to sell

at one’s price.

Conversely, it is easy to sell in a bid market and to buy in an offered market. It is possible to buy at the bid

price in a bid market or sell at the offer price in an offered market. This, however, depends on the

competence of the broker and, particularly, his ability to “read the market”. In any market there is often a

tendency for the market being “overdone”, i.e. a situation where price movements have been rapid, or

where profit taking takes place. This often results in a brief countertrend within the general trend. An

experienced broker would know where the “support” and “resistance” levels in the market are and when to

take action. Thus, the skill and knowledge of the broker are important in executing deals at the best prices.

When the broker executes a telephonic deal for a client with a counterparty (which is rare now with the

existence of the ATS) (assuming a deal in 10 contracts), he will say “10 yours” or “you’ve got 10” (in the case

of a sale) or “10 mine” or “I take 10” (in the case of a purchase). The broker will then “chalk” the deal on his

dealing pad and confirm the deal with the client (without disclosing the counterparty). The dealing pad

would record the details as shown in Table 3.14.

98

TABLE 3.14: DEALING PAD DETAILS

Time

Buy /

sell

Quantity

Contract

Expiry

Price

Counterparty

Name

11.00

11.05

Buy

Sell

10

10

ALSI

ALSI

March '05

March '05

25400

25402

ABC Broker

Mr. Bloggs

Lance

Mr. Bloggs

The dealing slip will record that the broker bought from Lance at ABC Broker 10 ALSI contracts at a price of

25 400 and sold 10 ALSI contracts to Mr. Bloggs at 25 402. The commission (which is negotiable) in this case

is 2 points, which is equal to R200 (R10 x 10 x 2).

The dealing sheet is then handed to the administration department for execution, i.e. the sending of

confirmation notes to the clients and for faxing to the clearing member. The clearing member, in turn,

“books” the deal to SAFEX/SAFCOM. (Note: as indicated earlier, the above example of a deal is rare in the

South African ATS-based market, but is included here because many international markets continue to

operate in this fashion.)

As noted earlier, SAFEX interposes itself between all buyers and sellers and thus guarantees all transactions.

All deals are thus matched by SAFEX. If mismatching does occur, this is conveyed to the broker concerned.

Mismatch reports are received by brokers early each morning and at noon. It will be evident that

mismatches can occur in terms of price, quantity, time, counterparty and buy/sell. It is notable that most

brokers record all transactions on tape. These recordings are used in the event of mismatches leading to

disputes. Disputes are resolved through arbitration.

Other important elements in the mechanics of dealing in futures are as follows:

• A broker will not execute a deal unless he has received the initial margin from the client and the

client has been registered by SAFEX.

• If a client does not meet a margin call, the broker will automatically “close the position” by doing an

opposite deal.

• A client can give a broker stop-loss orders, but the broker cannot guarantee the levels.

• Certain brokers also act as principals (i.e. take “positions” in futures, i.e. deal for “own account”).

They may thus take the opposite positions to clients. In this case they are obliged to convey this to

the client.

99

3.22 SIZE OF FUTURES MARKET IN SOUTH AFRICA

Table 3.15 provides a summary of the activity in the South African futures markets for a number of years.

TABLE 3.15: DERIVATIVE MARKET ACTIVITY

Year

Futures contracts other than on individual equities

and commodities

Individual

equity futures

contracts:

number of

contracts

Commodity

futures

contracts:

number of

contracts

Number of

deals

Number of

contracts

Underlying

value

(Rand

millions)

Open interest

(number last

business day)

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

161 967

131 322

163 078

125 806

158 144

174 018

132 575

166 508

606 912

624 262

694 118

1 038 911

1 233 253

4 095 410

5 189 824

7 402 500

9 076 146

9 182 363

11 333 675

10 256 935

13 292 576

18 247 582

35 176 298

85 625 757

296 885 064

413 672 641

266 130

349 401

460 325

590 802

757 594

901 187

800 254

743 550

997 701

1 501 428

2 899 227

4 723 222

4 676 293

90 349

166 854

163 674

184 920

241 030

227 466

256 420

491 062

908 218

1 831 406

12 346 070

32 432 319

14 881 733

-

-

-

8 2901

2 022 570

6 840 323

10 326 223

11 463 103

15 738 624

27 288 035

75 423 583

279 760 204

391 329 595

5 215

21 830

80 635

249 907

455 265

1 001 165

1 969 239

2 305 673

1 894 059

1 771 470

1 940 132

2 402 053

2 646 108

Source: South African Reserve Bank Quarterly Bulletin

100

3.23 ECONOMIC SIGNIFICANCE OF FUTURES MARKETS46



3.23.1 Introduction

There is not much debate amongst scholars of futures markets regarding the economic functions of these

markets, although the functions are described in different ways. The economic functions are as follows:

• Price discovery.

• Market liquidity.

• Market efficiency.

• Resource allocation.

• Capital formation.

• Output.

• Public welfare.

• Competition.

• New product development.

Although these functions are described separately below, they should not be seen in isolation but as

interdependent.

3.23.2 Price discovery

Futures markets have developed from the desire of participants in the financial and commodities markets to

hedge against the risk of adverse price changes in these markets in the future. Thus, there was a need for an

instrument to allow participants to hedge against unexpected cash market prices in the future.

As noted earlier, the theoretical futures price (fair value price) is made up of the cash market price plus the

net carry cost. It is also known that futures prices do not always equate to the theoretical price. Futures

prices can be substantially above the theoretical price (i.e. at a premium), at a discount to the theoretical

price and even at a discount to the cash market price. Clearly then, futures prices are not only influenced by

the cash market price plus net carry costs, but are also heavily influenced by expectations of price changes in

the underlying market.

Thus, the futures price is the outcome of the cash market price, the net carry cost and the perceptions of the

many participants in the futures market regarding the course of the cash market price in the future (i.e. the

futures price reflects all available information and the participants’ interpretation of this information). It can

thus be said that the futures market, at any point in time, “discovers” the cash market price in the future.

46 This section summarises the work of Collings, 1993.

101

The question that arises now is to what extent the futures price can be regarded as rational and correct. This

question is more pertinent the further away the expiry date of the futures contract. As shown, the futures

price converges with the cash market price and becomes zero at expiry date. Thus, the closer to expiry, the

more rational and correct the futures price is in terms of “discovering” the cash market price on expiry.

Controversy in the above regard abounds. The debate revolves mainly around:

• The determinants of price variability.

• The causality of price movements between the futures market and the cash market.

• The general economic consequences of price volatility.

Some scholars of the futures market believe that price volatility is an inherent characteristic of the futures

market and attracts speculators to the market. These speculators enhance liquidity, which is necessary for

the efficient functioning of the market; they thus contribute to rational and correct pricing. Critics, however,

believe that price volatility results from speculative activity and obstructs the process of price discovery.

As regards the causality of price movements, certain commentators believe that because futures prices are

based on perceptions of price changes in the cash market in the future, the causality is from the cash market

to the futures market. Critics, however, contend that futures market activities result in the causality being

reversed, i.e. prices in the futures market dictate price movements in the cash market.

Concerning the economic consequences of price volatility, some critics state that volatile futures prices are

transmitted to the underlying markets and cause distortions in the spot prices of these commodities. This

could have consequences for production.

However, as we saw above, there are commodity markets where the spot price is derived from the near

futures price. Thus it can be said that the futures market is essential for price discovery in the spot market.

3.23.3 Market liquidity

It is generally accepted that “liquidity” refers to the ease of entry and exit from a market. Futures markets

are generally very liquid for two main reasons:

They are “derived” from underlying markets which are generally liquid

Futures contracts are standardised and restricted in terms of expiry dates (i.e. there are not many contracts;

thus activity is not dispersed amongst many contracts).

It will be understood that if participants in the cash market expect adverse and/or volatile price changes in

this market, they may withhold from investing until the risk exposure is reduced to acceptable levels. Futures

contracts provide the means of reducing exposure, thus allowing the participant to enter the cash market

now. The existence of the futures market also encourages speculators and arbitrageurs to enter the cash

market. In general, the existence of an active futures market enhances liquidity in the cash market.

3.23.4 Market efficiency

Market efficiency has to do with prices fully reflecting all available information. This is the case if all

information is available to all participants at no cost, if there are no transaction costs and all participants are

in agreement with regard to the implications for price formation of current and future information.

102

Closely related to market efficiency is market liquidity. A market cannot be efficient if there is limited

competition (market participation). Wide market participation (i.e. intense competition) ensures that all

available information is reflected in the price. If prices reflect true economic values and the information

pertaining to them, capital in the market would be allocated correctly.

It will be evident that if a futures market is efficient, then it contributes to the efficient functioning of the

related markets (the closest relative is, of course, the underlying market). For example, an efficient futures

market reduces the cost of hedging and promotes the use of the underlying markets. This has benefits down

the line such as increased production and demand, increased inventory holdings, the encouragement of

specialisation (and resultant economies of scale), etc.

3.23.5 Allocation of resources

Closely related to market liquidity and efficiency is the allocation of resources (in fact, these should not be

separated). Certain students of the economics of futures markets (particularly commodity futures markets)

have indicated that the presence of a futures market for specific exhaustible resources increases the

allocative efficiency of that market. The argument is that when futures trading exist the market is broad and

contains more information. Prices are likely to be more efficient and resources are allocated more efficiently.

3.23.6 Capital formation

The effect of futures markets on capital formation is a contentious issue. The critics maintain that the

existence of futures markets redirects risk capital away from the underlying markets, thus impeding capital

formation. On the other hand, proponents agree that, by enabling producers to hedge, futures markets

enhance capital formation - through putting producers in a better situation in terms of planning future

production.

3.23.7 Output

Demand and supply fluctuations in an underlying market result in risk for producers. Uncertainty with regard

to future prices and demand could result in lower output (and capital formation). The existence of an

efficient futures market creates the opportunity for producers to relate output to demand (by utilising

appropriate hedging techniques). The futures market thus reduces and distributes the risk associated with

production and prices in the future - in this way contributing to increased output.

3.23.8 Competition

Certain commentators suggest that futures markets contribute to greater and more effective competition in

the underlying markets and thus to prices which are lower than they otherwise would be. This favourable

characteristic is believed to be transmitted to other related markets.

3.23.9 New product development

It is also maintained that the development of new products and services have been encouraged by the

introduction of futures markets. Firms are more likely to create new products if they are able to reduce the

risks and transaction costs involved (through hedging).

103

3.23.10 Public welfare

It is contended that the existence of efficient futures markets, through the effects on the underlying markets

in terms of price discovery, resource allocation, liquidity, competition, new product development and on the

output of firms, contributes to general public welfare.


Outcomes

• Define a futures contract.

• Understand the constituents of the definition of futures contracts.

• Understand the payoff (risk) profile of futures contracts.

• Understand the characteristics of the futures market, such as getting out of a position in futures, and

cash settlement versus physical settlement

• Understand the concepts of margins, marking to market and open interest.

• Comprehend the principles applied in the pricing of futures contracts (fair value).

• Calculate the fair value prices of futures contracts.

• Understand the concepts of convergence, basis and net carry cost in relation to basis.

• Understand the motivation for undertaking deals in futures, particularly hedging, and the

participants in the futures market.

Review questions

1. Futures can be bought and sold in the secondary market like NCDs or treasury bills. True or false?

2. A futures exchange is a “marketplace” where buyers and sellers can “find” each other to enter into a

futures contract. True or false?

3. In practice the delivery of the underlying asset on the expiry date of a futures contract is rare, particularly

in the financial futures markets. True or false?

4. A future will always trade at a value above the spot price of the underlying asset up to the expiry date,

when the two values will be the same. True or false?

5. At the start of a futures deal the "initial margin" deposit that has to be paid at the start of a futures deal is

set at a level that essentially protects the exchange from default because it is extremely unlikely that

losses on positions will exceed the initial margin. True or false?

6. In South Africa settlement of a financial futures contract can only be done in cash. True or false?

7. The fair value price of a short-term interest rate future cannot be calculated without an implied forward

rate. True or false?

8. The fair value price of a bond future is its clean price less the applicable interest factor. True or false?

9. What is the relationship between a futures contract on the one hand and specific and notional assets on

the other?

104

10. An investor bought an index future on 5 September 2005 with an expiry date of 30 September. The

trading price was 7535. The value of a contract was R10 times index value and the investor bought 5

contracts at a total transaction cost (commission) of R50. On 30 September the index value was 7685.

What was the total profit (+) or loss (–) to the investor?

11. What is a "short sale"?

12. Why are members of the futures exchange referred to generically as "broker-dealers"?

13. Why is each futures contract "valued" at the end of every working day?

14. Define "open interest" in the futures market.

15. Given the following information, what is the fair value price of an index future?

Spot price (SP) = 5375

risk free rate (rfr) (assumed) = 12.5% pa

assumed dividend yield = 2.1% pa

term to maturity of contract = 320 / 365.

16. The rate now (spot rate) for three months (91 days) is 7.9% pa, the rate now (spot rate) for six months

(182 days) is 8.2% pa, and the rate now for nine months (273 days) is 8.7% pa. What is the implied

forward rate for six months?

17. The price of a 3-month JIBAR interest rate future was 91.11 on the date the contract (nominal value R1

000 000) was purchased. On the expiry date the price of this future is 92.34. How much will the exchange

pay the client as settlement (into variation margin)? The minimum price movement (= tic) = 0.01.

18. You have the following information:

Bond = R157

Maturity date = 15 September 2015

Coupon (c) =13.5% pa

Coupon payment dates (cd1 and cd2) =15 March and 15 September

Yield to maturity (ytm) = 8.2%

Carry cost (CC) (= rfr) = 7.5% pa

Purchase (valuation) date of future (fvd) = 16 July

Termination date of future (ftd) = 16 October

Books (register) closes = one month before coupon dates

If the dirty price of the bond is 105.71077, what is the fair value price of the futures contact?

19. You are given the following information regarding an ALSI future:

SP (i.e. index value) = 11232

105

Rfr = 8.5% pa

I (dividend yield, assumed) = 3.5% pa

t (number of days to expiry of contract / 365) = 132 / 365

What is the fair value price of this future?

20. Summaries the concepts of "net carry cost" and "basis" in one equation that gives the fair value price in

terms of the spot price and these two concepts.

Answers

1. False. Futures are only marketable in the sense that they can be “closed out” by undertaking an opposite

transaction.

2. False. Even though a client may buy a future from, or sell a future to, a member of the exchange, the

transaction is guaranteed by the exchange, i.e. the exchange acts as the seller for each buyer, and as the

buyer for each seller.

3. True.

4. False. At times the future can trade at a discount to the spot price.

5. True.

6. False. In the financial futures markets, physical delivery also takes place in some cases (for example,

certain of the bond contracts), but in the majority of cases settlement takes place in the form of cash

settlement.

7. True.

8. False.

9. A futures contract is a derivative instrument, i.e. it and its value are derived from an underlying asset and

it cannot exist in the absence of this asset. The underlying assets of futures contracts can be divided into

two broad categories, i.e. specific assets and notional assets. Specific (also called “physical”) assets

include the R153 bond, pork bellies, etc, while notional assets include the industrial index, the all share

index, the gold index, etc.

10. R7 450 {[(7685 – 7535) x R10 x 5] – 50}.

11. “Short” sale means the sale of an instrument that the seller does not own. The seller borrows the

instrument from an investor / lender for a fee and delivers it back to the lender when the short sale is

unwound by the purchase of the instrument. A short sale is undertaken to profit opportunistically from

an expected decline in price.

12. Members of the futures exchange are referred to by the generic term broker-dealers, because they may

deal as principals or agents (in dual capacity). Some broker-dealers do not have clients and only deal as

principals, and some broker-dealers deal only as agents with clients (both are called single capacity).

106

13. The purpose of the marking to market is to ensure that the margin account is kept funded. If the mark to

market price is lower that the purchase price, i.e. if the holder of a future is making a loss, s/he has to top

up the margin account to the proportionate level it was. This amount is called the variation margin. If a

holder makes a profit, a credit to the margin account is made. The ultimate purpose is to ensure that the

exchange, which has taken on the risk of guaranteeing the trades, is protected.

14. “Open interest” is the term for the number of outstanding contracts, i.e. contracts that are still open and

obligated to be delivered (physical or cash settlement). Double counting is avoided in the number. If

broker-dealer A takes a position in a future and B takes the opposite position, open interest is equal to 1.

15. 5865 {5375 x {1 + [(0.125 – 0.021) x (320 / 365)]}}.

16. 8.92% pa {{[1+(0.087 x 273/365)]/[1+(0.079 x 91/365)] –1} x [365/(273 – 91)]}.

17. R3 075 - 123 tics x R25 [R1 000 000 x (3 / 12) x (0.01 / 100)].

18. 105.71077

+ 1.99837 {A x {(rfr / 100) x [(ftd – fvd) / 365]}}

6.79300 {(c / 2) x (1 + {(rfr / 100) x [(ftd – cd2) / 365)]})}

= 100.91614.

19. 11435 {11232 x {1 + [(0.085 – 0.035) x (132 / 365)]}}.

20. FVP = SP + B + (NCC – B).


Futures listed on Yield-X:


Futures listed on Safex:

http://www.safex.co.za/

Futures tutorial:

http://www.cbot.com

107

CHAPTER 4 : SWAPS




Chapter 2 Forwards

Chapter 3 Futures

Chapter 4 Swaps

Chapter 5 Options




• Define a swap.

• Know the different types of swaps.

• Understand the motivations underlying interest rate swaps.

• Understand how swaps are utilised in risk management.

• Know the variations on the main themes of swaps.

4.3 INTRODUCTION

Swaps emerged internationally in the early eighties, and the market has grown significantly. An attempt was

made in the early eighties in South Africa to kick-start the interest rate swap market, but few money market

benchmarks were available at that stage to underpin this new market. It was only in the middle nineties that

the swap market emerged in South Africa, and this was made possible by the creation and development of

acceptable benchmark money market rates.

A reminder of where we are in this discussion is provided in Figure 4.1. We cover swaps before options

because of the existence of options on swaps. This illustration shows that we find swaps in all the spot

financial markets.

A swap may be defined as an agreement between counterparties (usually two but there can be more parties

involved in some swaps) to exchange specific periodic cash flows in the future based on specified prices /

interest rates. The cash flow calculations are made with reference to an agreed notional amount (i.e. an

amount that is not exchanged). Swaps allow financial market participants to better manage risk in their

relevant preferred habitat markets.

108

debt market


forexmarket

commodity markets

equity market

money market

bond market



FUTURES

FORWARDS SWAPS


options on

futures


Swaps are a significant part of the financial markets and, as noted, are found in all the markets. The interest

rate swap has a leg in the money market and a leg in the bond market. Equity swaps have a leg in the equity

market and the other in the bond market (and sometimes the money market). Currency swaps (not to be

confused with foreign exchange swaps) have two legs in the foreign exchange market, but in different

geographic markets. Commodity swaps involve the exchange of a fixed price on a commodity for the spot

price (usually an average), and sometimes the transaction does not include the same commodity. The swap

market may be depicted as in Figure 4.2.

To this list may be added the credit risk swap, but as the compensation for the “protection buyer” is

contingent upon a “credit event”, it is more akin to an insurance policy, and will be discussed under the

“other derivatives” section.

The various swaps undertaken in the five markets are covered briefly below. Interest rate swaps dominate

and are given pole position, and we conclude with brief sections on the listed swaps in South Africa and the

organisation of the swap market. The following are the headings:

• Interest rate swaps.

• Currency swaps.

• Equity swaps.

• Commodity swaps.

• Listed swaps.

• Organisation of the swap market.

109

FINANCIAL AND COMMODITY SWAPS

INTEREST RATE SWAPS

debt market

forexmarket

money marketcommodities

marketbond market

equity market

CURRENCY SWAPS

COMMODITY SWAPS

EQUITY SWAPS

FINANCIAL MARKETS

Figure 4.2: swaps

4.4 INTEREST RATE SWAPS

4.4.1 Introduction

An interest rate swap entails the swapping of differing interest obligations between two parties via a

facilitator, usually a bank that focuses on this market (and makes a market in this market). It is an agreement

between two parties to exchange a series of fixed rate cash flows for a series of floating rate cash flows in

the same currency. These interest amounts are calculated with reference to a mutually agreed notional

amount. The notional amount is not exchanged between the parties.

The party that agrees to make fixed interest rate payments is called the buyer and the party that undertakes

to make floating rate payments is called the seller. These swaps are also called coupon swaps. When two

floating rates are exchanged they are called basis swaps. In fact, there are a variety of interest rate swaps,

and these are mentioned at the close of this section. The following sections are covered here:

• Motivation for interest rate swaps.

• Coupon swap: transforming a liability.

• Coupon swap: transforming an asset.

• Coupon swap: comparative advantage swap.

• Organisation of the swap market.

• Variations on the theme.

110

4.4.2 Motivation for interest rate swaps

The circumstances that give rise to interest rate swaps (IRSs) usually involve interest rate risk or comparative

advantage. The following main IRSs may be identified:

• Transforming a liability.

• Transforming an asset.

• Comparative advantage.

4.4.3 Coupon swap: transforming a liability

An example of an IRS that transforms a liability is shown in Figure 4.3.

Pays

12.0% pa

f ixed rate every 6 months

Paysf loating CP rate

every

91 days

Pays

12.1% pa

f ixed rate every6 months

COMPANY A

Borrows R100 million by

issuing 91-day commercial paper (CP)

(f loating rate)

COMPANY B

Borrows R100 million by

issuing 3-year corporate bonds

(f ixed rate)

INVESTORS

in R100 million Co A 91-day commercial

paper (f loating rate)

(the paper is rolled over every 91-days)

INVESTORS

in R100 million Co B 3-year corporate bonds

(f ixed rate)

R100 million

Pays

f loating cp

rate every91 days

R100 million

Pays

12% pa f ixed

rate every 6 months

AGREED

NOTIONAL AMOUNT

R100 MILLION

SWAP

BROKER-DEALER

(BANK)Paysf loating CP rate

every

91 days

Figure 4.3: interest rate swap example: transforming a liability

In this example Company A has borrowed R100 million through the issuing of 91-day commercial paper

(which is re-priced every 91 days at the then prevailing rate), while Company B has borrowed R100 million by

the issuing of corporate bonds at a fixed rate of 12% pa for a 3-year period. These borrowing habitats could

reflect the following:

Company A believes interest rates are going to move down or sideways. It therefore does not want to “lock

in” a rate for a long period, and wants to take advantage of rates declining if this does come about.

Company B is of the view that rates are about to rise and wishes to lock in a rate now for the next three

years.

Time passes and the two parties change their views. A sharp banker spots the changed views of the two

companies and puts the following deals to them:

111

Company A

• Company A and the bank enter into an interest rate swap agreement.

• Company A agrees to pay to the bank a fixed rate of 12.1% for the next three years, interest payable

six-monthly.

• The bank agrees to pay Company A the floating commercial paper rate every 91-days.

• The notional amount of the swap is R100 million.

Company B

• Company B and the bank enter into an interest rate swap agreement.

• Company B agrees to pay to the bank the commercial paper floating rate every 91 days.

• The bank agrees to pay to Company B paying a fixed rate of 12.0%, interest payable six-monthly.

• The notional amount of the swap is R100 million.

Because of their changed views, the deals are accepted by both companies. Company A’s obligation to pay

the 91-day commercial paper rate to the holders (which may be different in each rollover period) is matched

by the bank’s payment of the 91-day commercial paper rate to it. It is then left only with the obligation to

pay the fixed rate of 12.1% pa to the bank.

Conversely, Company B’s obligation to pay the fixed 12% pa to the investors in its paper is matched by the

bank’s obligation to pay the fixed 12% pa rate to it. Company B is thus left with the obligation to pay the 91-

day commercial paper rate to the bank.

The interest obligations of the bank match, with the exception that the bank earns 0.1% on the fixed interest

leg of the transaction (R100 000 per annum excluding compounding and present value calculations).

The mathematics of this deal is straightforward, and simply amounts to interest payments (i.e. cash flows)

over the three-year period. The cash flows are shown in Table 4.1.

Company A’s floating rate obligation is cancelled out by the matching payments from the bank, and

Company B’s fixed rate obligation is cancelled out by the payments from the bank. Company A thus over the

period of 3 years paid out a total of R36.3 million in interest, compared with Company B’s R38 032 876.73.

Thus, Company A’s amended interest rate view was correct, and it saved R1.7 million. Company B’s treasurer

should have stuck to his original view.

Counterparty risk

It is rare that counterparties in swap deals are able to find one another and do a deal to their mutual

satisfaction. If they do, the deal rests on the integrity of the two parties, i.e. they are each exposed to

counterparty risk. More generally, it is bankers that seek out these transactions.

112

TABLE 4.1: FIXED FOR FLOATING INTEREST RATE SWAP

(FIXED RATE = 12% PA)

Company A pays Company B

pays

Floating

rate (% pa)

assumed

Year 1

Day 0

Day 91 (91 days)

Day 182 (91 days)

Day 273 (91 days)

Day 365 (92 days)

Year 2

Day 91 (91 days)

Day 182 (91 days)

Day 273 (91 days)

Day 365 (92 days)

Year 3

Day 91 (91 days)

Day 182 (91 days)

Day 273 (91 days)

Day 365 (92 days)

-

6 050 000

6 050 000

6 050 000

6 050 000

6 050 000

6 050 000

-

2 966 849.32

2 991 780.82

3 066 575.34

3 166 301.37

3 241 095.89

3 365 753.43

3 490 410.96

3 427 945.21

3 340 821.92

3 116 438.36

2 991 780.82

2 867 123.29

-

11.9

12.0

12.3

12.7

13.0

13.5

14.0

13.6

13.4

12.5

12.0

11.5

Total 36 300 000 38 032 876.73

The banks then interpose themselves between the clients (principals), and undertake to receive and pay the

relevant interest amounts. Clearly, it is only the large banks that are able to do these deals, because the

counterparty of each principal is the intermediary bank (sometimes called the swap agent).

Fixed rates and floating rates

The above was an example of a plain vanilla swap. The floating rate used was the 91-day commercial paper

rate. Most swaps in reality involve other well-known benchmark rates, such as the LIBOR in the UK, the

Fedfunds rate in the US, the ROD or JIBAR rates in South Africa, and so on. The fixed leg is not benchmarked

because it is an agreed number.

4.4.4 Coupon swap: transforming an asset

In the example presented in Figure 4.4, Company A transforms its investment in 91-day commercial paper,

which is reprised every 91-days, into an 11.9% fixed rate investment. Company B does the reverse. In this

example the motivation for the deal was a change in interest rate views. It will be noted that there is a

mismatch in the timing of the interest payments. This does not have to be the case.

113

Figure 4.4: interest rate swap example: transforming an asset

COMPANY A

Has R100 million investment in

91-day CP(f loating rate)

COMPANY B

Has R100 million investment in 3-year

bonds at 12% pa (f ixed rate)

ISSUER OF R100 MILLION 91-DAY

COMMERCIAL PAPER

ISSUER OF R100 MILLION 3-YEAR

BONDS

Pays CP f loating

rate every 91 days

Pays12% pa f ixed rate every 6 months

Pays 12% f ixed rate

every6 months

AGREEDNOTIONAL AMOUNT

R100 MILLION

Pays CPf loating every

3 months

Pays 11.9%fixed rate

every6 months

Pays CPf loating every

3 months

SWAP BROKER-

DEALER (BANK)

4.4.5 Coupon swap: comparative advantage swap47

TABLE 4.2: EXAMPLE OF COMPARATIVE ADVANTAGE IRS

Rating Company 3-year fixed rate

(bond market)

Floating rate

(money market)

AAA

BBB

Company A

Company B

11.0%

12.0%

6-month JIBAR + 0.0%

6-month JIBAR + 0.5%

Difference (B – A) +1.0% + 0.5%

The comparative advantage motivation for a swap deal rests on the existence of a differential in borrowing

rates in different markets. An example is presented in Table 4.2.

Company A has an absolute advantage in both markets (as a result of the credit rating difference), i.e.

borrows at a lower rate in both markets. However, it will be evident that while Company B pays a higher rate

than Company A in both markets, it is “penalised” to a lesser extent in the money market than in the bond

market (which could be because of the lower probability of default in the short-term). On the other hand,

Company A pays less in the bond market than in the money market when compared with Company B.

Thus, Company A has a comparative advantage in the bond market, while Company B has a comparative

advantage in the money market.

47 It is to be noted that the comparative advantage swap is almost extinct in the more sophisticated financial markets; this is because

the differentials that exists will be arbitraged out or not exist in the first place because, clearly, incorrect credit risk pricing has

occurred.

114

Important assumptions have to be made in this example:

• Company A wants to borrow floating.

• Company B wants to borrow fixed.

An astute banker sees the opportunity and proposes the following deal:

• Company A borrows in the market where it has a comparative advantage in relation to Company B

(bond market).

• Company B borrows in the market where it has a comparative advantage in relation to Company A

(money market).

The deal is accepted and the IRS then takes place as illustrated in Figure 4.5.

Figure 4.5: interest rate swap example: comparative advantage

Pays11.3% f ixed

every6 months

Pays11.2% f ixed

every6 months

Pays 11%f ixed rate

every

6 months

COMPANY A

Borrows R100 million by issuing 3-year corporate

bonds(11% pa f ixed)

COMPANY B

Borrows R100 million by issuing

6-month CP(f loating rate)

INVESTORS

in R100 million Co A 3-year corporate bonds

(11% pa f ixed)

INVESTORS

in R100 million Co B 6-month CP

(f loating rate)

AGREEDNOTIONAL AMOUNT

R100 MILLION

SWAP BROKER-

DEALER (BANK)

Pays6-m JIBAR

every6 months

Pays6-m JIBAR

every 6 months

Pays 6-mJIBAR + 0.5% every 6

months

The details of the transaction supplied in Table 4.3 should be apparent.

TABLE 4.3: EXAMPLE OF COMPARATIVE ADVANTAGE IRS: INTEREST PAYMENTS

Company Wanted to

borrow

Borrows (paying to

investors) Receives

Paying to

bank

Actually

paying

A floating @ 6-m

JIBAR fixed @ 11% 11.2% fixed 6-m JIBAR

6-m JIBAR

– 0.2%

B

fixed @ 12%

floating @ 6-m

JIBAR + 0.5%

JIBAR

11.3% fixed

11.3% + 0.5%

Bank 0.1% (net)

115

Company A borrows out of its preferred habitat (floating rate), but the swap synthesises the preferred

habitat, and the company benefits by 0.2%. Company B wants to borrow fixed, but borrows floating every 6

months for 3 years at 6-month JIBAR + 0.5%. It receives 6-month JIBAR, and therefore makes a loss on this

leg of 0.5%. It however pays 11.3% fixed to the bank, making its total cost 11.8%, which is 0.2% lower than

the fixed rate it would have paid in the bond market for its 3-year paper. The banker pockets 0.1% pa on

R100 million for 3 years (R100 000 per year).

4.4.6 Variations on the theme

There are many variations on the main IRS theme. A few examples are:

• Basis swap: A swap where two floating rates are swapped.

• Amortising swap: A swap with a notional value that reduces over the life of the swap in a

predetermined way.

• Accreting swap (also called step-up swap): A swap in terms of which the notional amount increases

in a predetermined manner during the term of the swap.

• Roller-coaster swap: A swap in terms of which the notional amount increases and decreases during

the term of the swap.

• Deferred swap (also called forward start swap): A swap where the counterparties do not start

exchanging interest payments until a future date.

• Extendable swap: A swap where one party has the option to extend the life of the swap beyond the

term of the swap, according to predetermined conditions.

• Puttable swap: A swap where one party has the option to terminate the swap prior to maturity date,

according to predetermined conditions.

• Constant maturity swap: A swap where a floating rate (for example LIBOR) is exchanged for a

specific rate (for example the 10-year rate on government bonds).

• Index amortizing rate swap (also called indexed principal swap): A swap where the notional amount

reduces in a way that is dependent on the level of interest rates.

• Timing-mismatched swap: A swap with a timing mismatch.

4.5 CURRENCY SWAPS


IN THIS SECTION ON “CURRENCY SWAPS” THE STUDENT WILL ONLY BE REQUIRED TO MASTER DEFINITIONS

(IE WILL NOT BE REQUIRED TO CALCULATE AMOUNTS BASED ON AN EXAMPLE)

4.5.1 Definition

A currency swap in its simplest form involves the exchange of principal and interest payments in one

currency for principal and interest payments in another currency. The amounts involved are usually of equal

magnitude and they are exchanged with interest at the beginning and the end of the life of the swap. The

following currency swaps are covered here:

• Simple currency swap.

• Comparative advantage currency swap.


116

4.5.2 Simple currency swap

Our first example of a swap is a simple one (see Figure 4.7; assumption: starting exchange rate = GBP / USD

1.5).

UK COMPANY

(Has f ixed-rate

GBP assets)

US COMPANY

(Has f ixed-rate

USD assets)

T + 0Borrows

USD 150 million

at 10% f ixed-rate for 2 years

T + 0Borrows

GBP 100 million

at 10% f ixed-rate for 2 years

LENDER

Is concerned

GBP will depreciate

Is concerned

USD will depreciate

T + 1 year T + 1 year

LENDER

USD 150 million

T + 1 year T + 1 yearGBP 100 million

T + 2 years T + 2 years

USD 150 million + interest = USD 15 million

GBP 100 million + interest = GBP 10 million

USD

150 million

GBP

100 million

GBP

110 million

USD

165 million

Figure 4.7: example of currency swap

The UK financial intermediary company has all its assets in UK pounds, but has GBP 100 million of its

liabilities in USD (2-year 10% pa fixed bond issue in USD = USD 150 million). In a similar fashion, a US

financial intermediary has all its assets in USD but has USD 150 million of GBP liabilities (2-year 10% pa fixed

GBP-denominated bond = GBP 100 million). Interest on both bonds is payable annually.

After a year the UK intermediary becomes concerned that the GBP will depreciate in relation to the USD and

it will have to service the debt (interest and principal) with more pounds in the future. At the same time the

US intermediary becomes concerned that the USD is about to depreciate in relation to the GBP, and that it

will have to service its UK pound debt (interest and principal) with depreciated dollars.

There is always a smart banker that will spot this “opposing currency risk condition”. He proposes the deal as

illustrated in Figure 4.7, and takes a “small” turn in one of the legs (which we ignore here for the sake of

simplicity).

The swap is done for principal and interest and the relevant amounts change hands at T+1 year. At T+2

(expiry of the swap and the bonds) the amounts plus interest are exchanged again in order for the debtors to

repay the creditors the principal plus interest amounts.

If at T+2 the exchange rate is GBP / USD 1.4, i.e. the GBP has depreciated (less USD per GBP or more GBP per

dollar: 1 / 1.4 = 0.71429 GBP per USD, compared with 1 / 1.5 = 0.66667 GBP per USD), the UK company is

better off than it would have been in the absence of the swap, with the position of the US company being

the converse. In the absence of the swap the UK company would have had to buy USD 165 million for GBP

117.86 million (1 / 1.4 x USD 150 million),compared with GBP 110 million it paid. The US company would

have been better off had the swap not been undertaken: it would have bought GBP 110 for USD 154 million

(1.4 x GBP 110 million), compared with USD 165 million it paid.

117

The above is an example where the currency swap transmutes liabilities from one currency to

another, with the purpose of managing currency risk. Another example is where a comparative

advantage exists. This follows.

4.5.3 Comparative advantage currency swap

LIBOR + 0.25% on $150m

LIBOR + 0.25% on $150m

@ 8% on £100m

Figure 4.8: example of currency swap

UKCO GERCO$150m @

LIBOR + 0.75%£100m f ixed

@ 8.5%

BORROWINGTERMS AVAIABLE

£100m f ixed@ 8%

$150m @ LIBOR + 0.25%

UKCO GERCOBORROW

UKCO -borrow $150m f loating

GERCO –borrow £100m f ixed

WANT TO$150m

investment in US

£100m investment

in UK

£100m

UKCO GERCOTHE SWAP$150m

@ 8% on £100m

UKCO GERCOPERIODIC EXCHANGE OF INTEREST

EXCHANGE OF PRINCIPAL ON EXPIRY

£100m UKCO GERCO

$150m $150m

£100m

The second example48

e is more realistic and is illustrated in Figure 4.8.

Wants / needs:

A UK company (UKCO) wants to borrow USD 150 million at a floating rate for 10 years in order to make an

investment in the US. A German company wants to raise GBP 100 million for 10 years at a fixed rate for

investment in the UK. The exchange rate is GBP / USD 1.5.

The following terms are available to them:

• UKCO: USD 150 million at LIBOR + 0.75%.

• GERCO: GBP 100 million at 8.5% fixed.

48 Example borrowed from Pilbeam, 1998.

118

Prelude to swap:

Their banker (they happen to have the same bank as their advisor) advises them that they should not borrow

on these terms, but rather as follows which they are able to:

• UKCO: borrow GBP 100 million at a fixed rate of 8% for 10 years.

• GERCO: borrow USD 150 million at LIBOR + 0.25%.

and that they simultaneously undertake to swap the principal and the obligations (interest is payable every

six months). It is evident that if they exchange debt obligations, their wants will be satisfied and they will be

borrowing at a lower rate.

A summary of the borrowing terms is given in Table 4.4.

TABLE 4.4: EXAMPLE OF COMPARATIVE ADVANTAGE CURRENCY SWAP: INTEREST PAYMENTS

Company USD rate GBP rate Wants to borrow

in:

Actually borrows

in:

UKCO LIBOR + 0.75 Fixed rate 8% pa USD GBP

GERCO

LIBOR + 0.25

Fixed rate 8.5% pa GBP USD

Each party has an advantage in a market compared with the other party: UKCO in the GBP market and

GERCO in the USD market.

Borrowing and the swap:

UKCO and GERCO see the advantages, accept the terms, borrow as advised, and the swap takes place. Each

is able to make their desired investment as follows:

• UKCO: investment of USD 150 million

• GERCO: investment of GBP 100 million.

The periodic exchange of interest:

The following cash flows take place over the period of 10 years (interest is payable every six months):

UKCO

• Pay: 8% fixed rate on GBP 100m (to holders of securities)

• Receive: 8% fixed rate on GBP 100m (from GERCO)

• Pay: LIBOR + 0.25% on USD 150m (to GERCO).

GERCO

• Pay: LIBOR + 0.25% on USD 150m (to holders of securities)

• Receive: LIBOR + 0.25% on USD 150m (from UKCO)

• Pay: 8% fixed rate on GBP 100m (to UKCO).

119

Exchange of principal on expiry of contract:

At expiry of the swap the principal amounts are exchanged as follows:

• UKCO: USD 150 million to GERCO

• GERCO: GBP 100 million to UKCO.

They are able to repay the holders of the securities they issued.

Net result:

The net result of the swap is that UKCO gets to borrow in its preferred habitat: USD 150 million at LIBOR, but

it borrows at a cheaper rate (i.e. LIBOR + 0.25% as opposed to LIBOR + 0.75%). Similarly, GERCO borrows

where it wanted to (GBP 100 million in the UK at a fixed rate), but also at a cheaper rate (8.0% fixed as

opposed to 8.5% fixed).

It is to be noted that the interposition of the bank was left out in the numbers. It will be evident that the

savings by each party allow for the banker to take a “healthy” turn. The banker was excluded because of the

extra arrows that would have rendered the illustrations untidy.


There are variations on the main theme of currency swaps, but not as many as in the case of interest rate

swaps. One of them is the cross currency swap (also called currency coupon swap). It involves the exchange

of a floating rate in one currency for a fixed rate in another currency. This is essentially a hybrid of the

currency swap and the plain vanilla interest rate swap.

Another is the differential swap (also termed the diff swap), which involves the exchange of a floating rate in

the domestic currency for a floating rate in a foreign currency. Both payments are referenced against a

domestic notional amount.

4.6 EQUITY SWAPS

4.6.1 Introduction

An equity swap is a fixed-for-equity swap. It is similar to the conventional interest rate swap in terms of a

term to maturity, notional principal amount, specified payment intervals and dates, fixed rate and floating

rate. The difference lies therein that the floating rate is linked to the return on a specified share index

(usually total return, i.e. capital appreciation and dividend). The following are the sections covered here:

• Example of equity swap.


120

Pays12.0% pa f ixed rate

every 6 months

Figure 4.9: example of an equity swap

PENSION FUND A

PENSION FUND B

Paysreturn on all share index every 6 months

Pays12.2% pa f ixed rate

every 6 months

AGREEDNOTIONAL AMOUNT:

R100 MILLION

AGREED PERIOD:2 YEARS

INTERMEDIARY BANK

Paysreturn on all share index every 6 months

View: equity performance poor

for next 2 years

View: bond performance poor

for next 2 years

4.6.2 Example of equity swap

These swaps are a relatively new invention (first emerged in 1989), and are used for temporary desired

changes to the income of a portfolio without having to sell the relevant instrument/s. For example (see

Figure 4.9), a portfolio manager may believe that equities are to yield inferior returns for, say, two years, and

that over this period bonds should perform well. An equity swap is an ideal instrument for this purpose, i.e.

the equity return is swapped for a fixed rate of return for two years.

It will have been noted that the intermediary bank (who arranged the deal) profits by 0.2% pa on the fixed

leg (R200 000 pa for 2 years). The two principals (pension funds) are not aware of this because they deal

with the bank.


There are some variations to this plain vanilla equity swap:

• Floating-for-equity equity swap: An equity swap with one leg benchmarked against a floating rate of

interest and the other leg benchmarked against an equity index.

• Asset allocation equity swap: An equity swap where the equity leg is benchmarked against the

greater of two equity indices.

• Quantro equity swap: An equity swap with two equity legs, the return on one equity index is

swapped for the return on another equity index.

• Blended-index equity swap: An equity swap where the floating leg is an average (weighted or

otherwise) of two or more equity indices.

• Rainbow-blended-index equity swap: Same as the previous, but the indices are different foreign

indices.

121

4.7 COMMODITY SWAPS

Commodity swaps are where parties exchange fixed for floating prices on a stipulated quantity of a

commodity (for example a 20 000 ounces of platinum). An example: a South African producer of platinum

wishes to fix a price on part of its production (20 000 ounces), because it is of the opinion that the price of

platinum is about to fall (wants to receive fixed, i.e. a fixed price, and pay floating, i.e. the spot rate).

On the other hand, a manufacturer of jewellery in Italy believes that the price of platinum is about to rise

sharply (wants to pay fixed, i.e. fixed price, and receive floating, i.e. spot price).

An on-the-ball intermediary bank spots this difference of opinion and puts together the following deal (spot

price at inception of the deal is USD 1 529 per ounce):

The bank offers the mine a fixed price of USD 1 528 per ounce for the next 2 years, payable monthly, in

exchange for monthly payments of the average spot rate for the preceding month.

The bank offers the jewellery manufacturer monthly payments of the average spot rate for the preceding

month, in exchange for a fixed price of USD 1 530 per ounce for the next 2 years, payable monthly.

Both parties cannot believe their good fortune and accept the deal. The banker is also pleased. It will be

apparent that if the platinum price falls, the mine will be extremely pleased, because it receives the ever-

declining price on the spot market and pays this to the intermediary bank. In exchange the miner receives

the fixed price of $1 528 per ounce.

Figure 4.10: example of a commodity swap

PLATINUM MINE (believes platinum

price will fall)

PLATINUM SPOT MARKET

JEWELLARY MANUFACTURER (believes platinum

price will rise)

AGREED NOTIONAL AMOUNT: ONE TON PLATINUM

AGREED PERIOD:

TWO YEARS

INTERMEDIARY BANK

$1 528Pays spot price

$1 530Receives

spot pricePays spot price

Receives spot price

Sells platinum

Buys platinum

The jewellery manufacturer, on the other hand, will be smarting because it is paying floating in the spot

market and receiving this same amount, while paying a fixed price that is increasingly higher than the spot

price. The opposite case will be obvious. This swap deal is depicted in Figure 4.10.

122

4.8 LISTED SWAPS

Generally speaking the swap market is an OTC market “made” by the banks (see next section). However, in

certain markets listed swaps are listed on financial exchanges. In South Africa, for example, the following

listed swaps are found:

• Vanilla swaps.

• Coupon swaps.

• On demand swaps.

• j-Swaps.

• j-Rods.

Vanilla swaps are “normal” fixed for floating swaps, where a fixed rate is swapped against the 3-month JIBAR

rate.

Coupon swaps are swaps where bond coupons are swapped against the 3-month JIBAR plus a spread. There

is a coupon swap product for each of the popular RSA bonds.

On demand swaps are swap contracts listed on request by market participants. They are the non-vanilla

swaps or vanilla swaps with broken periods. The maturity of these swaps and reset frequency vary according

to request.

J-swaps are swaps of a NACS (Nominal Annual Compounded Semi-annually) 6-month interest

rate (the fixed side of the swap) against the 3-month JIBAR rate. They are also called “Bond look-

alike swaps”.

J-Rods are swaps of the Rand Overnight Deposit Interest Rate (RODI), as determined by the JSE, against a

fixed rate; there are 12 j-Rods contracts at all times, one for each month.

4.9 ORGANISATIONAL STRUCTURE OF SWAP MARKET

As noted, the swap market is largely an OTC market and it is dominated by the banks. As such, it is largely a

primary market. As in the case of OTC forwards, the OTC swaps are difficult to sell and “getting out” of them

amounts to finding an equal and opposite OTC deal (which is not always easy to find).

This also applies to the listed swap market, but there is a major difference: the contracts are standardised,

and exchange-traded, and trading “out” of them is easier. Another advantage is that the exchange

guarantees the swap deals.

In the OTC swap market the trading driver is “quote” (mainly done by the banks) whereas in the exchange-

driven market participants place orders with their broker-dealers. The trading system in the OTC market is

screen / telephone, i.e. firm prices are quoted on screen and confirmed on the telephone. In the exchange-

driven markets it is a combination of ATS and screen-telephone.

123

Market nature

PRIMARY MARKET

Market form

Market type

Trading driver

Trading system


Trading form

ORDER QUOTE

OTC EXCHANGE

FLOOR TEL / SCREEN

ATSSCREEN / TEL

SINGLE CAPACITY

DUAL CAPACITY



Outcomes

• Define a swap.

• Know the different types of swaps.

• Understand the motivations underlying interest rate swaps.

• Understand how swaps are utilised in risk management.

• Know the variations on the main themes of swaps.

Review questions

1. The agreed notional amount in a swap is exchanged at the start of the swap and at the maturity of the

swap. True or false?

2. The party that agrees to make fixed interest rate payments is called the buyer and the party that

undertakes to make floating rate payments is called the seller. True or false?

3. The three main reasons for an interest rate swap are: transforming a liability, transforming an asset and

speculation. True or false?

4. The intermediary bank that arranges a swap transaction assumes the counterparty risk because it

interposes itself between the clients (the two parties to the swap), and undertakes to receive and pay the

relevant interest amounts. True or false?

5. Most swaps in reality involve well known benchmark rates, such as the LIBOR in the UK, the Fed funds

rate in the US, the ROD or JIBAR rates in South Africa, and so on, which the fixed and floating rates in the

swap are based in each payment period. True or false?

124

6. Comparative advantage will exist when the one party in the exchange has an absolute advantage in one

market and the other party an absolute advantage in the other market. True or false?

7. A basis swap is where two floating rates are swapped. True or false?

8. A currency swap in its simplest form involves the exchange of interest payments in one currency for

interest payments in another currency. True or false?

9. Define a swap.

10. What is a swap called when two floating rates are exchanged?

11. Company A has borrowed R1 million through the issuing of 91-day commercial paper (which is re-priced

every 91 days at the then prevailing rate), while Company B has borrowed R1 million by the issuing of

corporate bonds at a fixed rate of 8.0% pa for a 3-year period. A bank now arranges a swap between the

parties who agrees that the bank will earn 0.1% on the fixed interest leg of the transaction. Assume a

floating rate for the first two 91-day periods after the swap agreement of 8.5 and 8.6 respectively. What

amounts will Company A and Company B pay to the bank in each of these first two months?

12. Company A has invested R1 million in 91-day commercial paper (which is re-priced every 91 days at the

then prevailing rate), while Company B has invested R1 million in corporate bonds at a fixed rate of 8.0%

pa for a 3-year period. A bank now arranges a swap between the parties who agree that the bank will

earn 0.1% on the fixed interest leg of the transaction. Assume a floating rate for the first two 91-day

periods after the swap agreement of 8.5 and 8.6 respectively. What amounts will Company A and

Company B receive from the bank in each of these first two months?

13. Two companies can borrow as follows:

Fixed market Floating market

Company A 6.5 6.9

Company B 5.4 5.5

Which company has got an absolute advantage in the fixed market and how big is that advantage? Which

company has got an absolute advantage in the floating market and how big is that advantage?



Company A 6.5 6.9

Company B 5.4 5.5

Which company has a comparative advantage in the fixed market and how big is that advantage? Which

company has a comparative advantage in the floating market and how big is that advantage?

125



Company A 6.5 6.9

Company B 5.4 5.5

What is the potential gain to be derived from a swap (and which will have to be shared by the parties to the

swap arrangement)? If the gain is shared equally after the bank that arranged the swap has taken a

commission of 0.1%, what rate will each party end up paying the bank (assuming that this rate is adjusted to

apportion the gain correctly and assuming the floating rate doesn't change)?

The UK financial intermediary company has GBP 100 million of its liabilities in USD (2-year 10% pa fixed bond

issue in USD = USD 180 million). In a similar fashion, a US financial intermediary has USD 180 million of GBP

liabilities (2-year 10% pa fixed GBP-denominated bond = GBP 100 million). Interest on both bonds is payable

annually. A currency swap is done for two years at the exchange rate applicable at the time. If at the end of

year 2 the exchange rate is 1.9 USD for 1 GBP, i.e. the GBP has appreciated (more USD per GBP), how much

did the UK company gain or lose from the swap?

A SA company (SACO) wants to borrow USD 100 million at a floating rate for 10 years in order to make an

investment in the US. A US company (USCO) wants to raise ZAR 650 million for 10 years at a fixed rate for

investment in SA. The exchange rate is ZAR 6.5 to one USD. The following terms are available to them:

• SACO: USD 100 million at LIBOR + 0.75%

• USCO: ZAR 650 million at 7.5% fixed.

Their banker advises them that they should not borrow on these terms, but rather as follows which they are

able to:

• SACO: borrow USD 100 million at a fixed rate of 7% for 10 years

• USCO: borrow ZAR 650 million at LIBOR + 0.25%

and that they simultaneously undertake to swap the principal and the obligations (interest is payable every

six months). They borrow as advised, and the swap takes place. Assume that each of the two parties gives up

0.1% of its benefit from the swap to pay the 0.2% commission that the bank charges for arranging the swap.

What is the net interest rate that each will pay every six months after the swap?

16. Define a cross currency swap.

126

17. Investor A has R100 million invested in government bonds at 9.6% pa, payable every six months, but

would prefer to get a return on equity for the next two years. Investor B has got R100 million invested in

equity, but would prefer a fixed return for the next two years. A bank arranges an equity swap at a

commission of 0.2%. What will be the cash flows (in return terms, not in rand) to and from the bank for

the two investors every six months?

18. A SA maize producer wishes to fix the price on 100 tons of the coming season's production. A SA mill

wants to fix the price on 100 tons of maize that it will require in the coming season for its milling

operations. What will be the price expectations of the two parties for a swap to be desirable?

Answers

1. False. The notional amount is not exchanged.

2. True.

3. False. The main motivations for an interest rate swap are transforming a liability, transforming an asset

and comparative advantage.

4. True.

5. False. The fixed leg is not benchmarked because it is an agreed number.

6. False. One party may have (and often does) an absolute advantage in both markets. Comparative

advantage is possible if there is a relative difference in the absolute advantage that the one party might

have in the two markets.

7. True.

8. False. A currency swap in its simplest form involves the exchange of principal and interest payments in

one currency for principal and interest payments in another currency.

9. A swap may be defined as an agreement between counterparties (usually two but there can be more

parties involved in some swaps) to exchange specific periodic cash flows in the future based on underlying

assets or prices. The interest calculations are made with reference to an agreed notional amount.

10. A basis swap.

11. First 3-month period:

Company A pays bank: R0 {fixed interest is paid every six months}

Company B pays bank: R21 192 {1 000 000 x [0.085 x (91 / 365)]}

Second 3-month period:

Company A pays bank: R40 500 {1 000 000 x [(0.081 / 2)]}

Company B pays bank: R21 441 {1 000 000 x [0.086 (91 / 365)]}.

127

12. First 3-month period, receipts from bank:

Company A receives: R0 {fixed interest is paid every six months}

Company B receives: R21 192 {1 000 000 x [0.085 x (91 / 365)]}

Second 3-month period, receipts from bank:

Company A receives: R39 500 {1 000 000 x [(0.079 / 2)]}

Company B receives: R21 441 {1 000 000 x [0.086 (91 / 365)]}

13. Company B has an absolute advantage in the fixed market; the advantage is 1.1% pa (= 6.5 – 5.4).

Company B has an absolute advantage in the floating market; the advantage is 1.4% pa (= 6.9 – 5.5).

14. Company B has a comparative advantage in the floating market: it is able to borrow at 1.4% pa lower

than Company A compared to 1.1% pa lower than Company A in the fixed market (a difference of 0.3%

pa.). Company A has a comparative advantage in the fixed market: it is able to borrow at 1.1% pa higher

than Company B compared to 1.4% pa higher than Company B in the floating market (a difference of

0.3% pa).

15. The potential gain from a comparative advantage swap is 0.3% (= 1.4 – 1.1). The bank will receive 0.1% of

this leaving 0.2% to be shared equally by A and B. Each one will therefore gain 0.1%. Company A will

initially borrow in the fixed market but will pay the bank after the swap a floating rate of 6.8%. Company

B will initially borrow in the floating market but will pay the bank after the swap a fixed rate of 5.3%.

16. The UK company is worse off than it would have been in the absence of the swap. In the absence of the

swap the UK company would have had to buy USD 198 million for GBP 104.21 million (1 / 1.9 x USD 198

million),compared with GBP 110 million (1 / 1.8 x USD 198 million) it paid with the swap.

17. Net interest rate paid by SACO: LIBOR + 0.35% on USD 100m.

Net interest rate paid by USCO: 7.1% fixed rate on ZAR 650m.

18. A cross currency swap (also called currency coupon swap) involves the exchange of a floating rate in one

currency for a fixed rate in another currency.

19. Investor A:

Payment to bank: 9.6% pa fixed rate every six months

Payment by bank: return on all share index every six months.

Investor B:

Payment to bank: return on all share index every six months

Payment by bank: 9.4% pa fixed rate every six months.

128

20. The maize producer wishes to fix a price on its production (100 tons), because it is of the opinion that the

price of maize is about to fall (wants to receive fixed, i.e. a fixed price, and pay floating, i.e. the spot rate).

On the other hand, the miller who has to buy the maize believes that the price of maize is about to rise

sharply (wants to pay fixed, i.e. fixed price, and receive floating, i.e. spot price).


Swap products listed on BESA:

http://www.bondexchange.co.za/besa/action/media/downloadFile?media_fileid+2887

Swap products listed on Yield-X:


129

CHAPTER 5: OPTIONS




Chapter 2 Forwards

Chapter 3 Futures

Chapter 4 Swaps

Chapter 5 Options




• Define an option.

• Understand the characteristics of an option.

• Know the different types of, and concepts relating to options.

• Understand the payoff profiles of the various option types.

• Comprehend intrinsic value and time value.

• Understand the motivation for undertaking (buying or writing) option contracts.

5.3 INTRODUCTION

Our depiction of the derivatives markets and their relationship to the spot markets is shown here again for

the purpose of orientation (see Figure 5.1). The figure shows that there exist options on specific instruments

(called “physicals”) in the various financial markets and the commodities market, and options on other

derivatives, i.e. futures, and swaps (with the exception of the category “other”). However, Figure 5.1 cannot

demonstrate the detail of the options markets; this is portrayed in Figure 5.2.

130

debt market


forexmarket

commodity markets

equity market

money market

bond market



FUTURES

FORWARDS SWAPS


options on

futures


OPTIONS

debt market

forexmarket


marketbond market

equity market

SWAPSFORWARDS FUTURES

OTHER DERIVATIVE INSTRUMENTS FINANCIAL MARKETS

SPECIFIC (“PHYSICAL”) INSTRUMENTS AND NOTIONAL INSTRUMENTS (INDICES)

Figure 5.2: options

Figure 5.2 show that there exist options on the derivatives futures and swaps (called swaptions), and that

there are options on specific instruments and indices in the various financial markets and the commodity

markets. These are covered in the following sections:

131

• The basics of options.

• Intrinsic value and time value.

• Option valuation and pricing.

• Organisation of options markets.

• Options on derivatives: futures.

• Options on derivatives: swaps.

• Options on debt market instruments.

• Options on equity market instruments.

• Options on foreign exchange.

• Options on commodities.

• Option strategies.

• Exotic options.

5.4 THE BASICS OF OPTIONS

5.4.1 Introduction and definitions

An option bestows upon the holder the right, but not the obligation, to buy or sell the asset underlying the

option at a predetermined price during or at the end of a specified period. Holders exercise their options only

if it is rewarding to do so, and their potential profit is not finite, while their potential loss is limited to the

premium paid for the option.

There are two parties to each option: the writer and the owner or holder. The writer grants the rights that

the option bestows on the owner.

There are three brands of options, i.e. American, European and Bermudan:

• An American option bestows the right upon the holder to exercise the option at any time before and

on the expiry date of the option.

• A European option gives the holder to exercise the option only on the expiry date of the option.

• A Bermudan option is an option where early exercise is restricted to certain dates during the life of

the option. It derives its name from the fact that its exercise characteristics are somewhere between

those of the American (exercisable at any time during the life of the option) and the European

(exercisable only at the expiration of the option) style of options.

The majority of options traded locally and internationally is American options. It is to be noted that the three

option brands do not refer to a geographic location. American and Bermudan options exist in Europe and

European and Bermudan options can be found in America.

Options are classified as call options and put options:

• The call option bestows upon the purchaser the right to buy (think “call for …”) the underlying asset

at the pre-specified price or rate from the writer of the option.

• The put option gives the holder the option to sell the underlying asset at the pre-specified price or

rate to the writer (think “put the writer with …”).

The buyer pays the writer of the option an amount of money called the premium. It is called this because an

option is much like an insurance policy.

132

Thus, there are two sides to every option contract (in the primary market):

• The buyer who has taken a long position, i.e. he has bought the option and has the benefits of the

option (the “option” to do something). The buyer pays the premium for the option to the seller.

• The seller who has taken a short position, i.e. he has sold the option and received the premium (the

seller has “no options” but is contracted to do something if the buyer decides to exercise the

option). The seller of an option is the writer of the option.

The terms long position and short position applies to both puts and calls, i.e. one can have a long put and a

long call (see below). It will be apparent that the writer’s “position” is the reverse of that of the buyer of the

option. If the writer does not have an offsetting position in the underlying market, he is said to be naked or

uncovered. If the writer does then he is covered.

Options are said to be in-the-money (ITM), at-the-money (ATM) and out-the-money (OTM) (obviously from

the point of view of the holder) as follows (in the case of call options):

• ITM: Price of underlying asset > strike price

• ATM: Price of underlying asset = strike price

• OTM: Price of underlying asset < strike price.

Another few parts of the definition require further illumination:

• underlying asset

• exercising

• exercise price

• expiration

• lapse

Options are written on “something”. This “something” is anything, i.e. options can be written on anything. As

each house buyer and seller knows, the most common option is an option to buy a house. The seller of the

house gives (writes) the option to the potential buyer of the house to buy the house at a specified price

(exercise or strike price) during a specified period.

The house option is usually written free of charge (i.e. no premium is payable), and has a fixed term of a day

or two or three. The holder of the option can exercise the option at any time between the time of the writing

of the option and the expiration of the option at the strike (or exercise) price (i.e. specified price). The option

lapses if the holder decides to not exercise his rights under the option. If the buyer exercises the option, the

seller is obliged to do the deal, i.e. deliver the underlying asset (the house).

As seen earlier, the underlying assets in the options markets of the world are other derivatives (futures and

swaps), and specific instruments (“physicals”) and notional instruments (indices) of the various markets.

5.4.2 Payoff profiles

There are 8 possibilities in terms of profit and/or losses when the price of the underlying asset changes

(simple assumption: strike price = price of underlying). They are as shown in Table 5.1.

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TABLE 5.1: PAYOFF PROFILES OF WRITER AND BUYER

Position Change in price of

underlying asset Profit or loss

Call option – buy (long call)

Call option – sell (write) (short call)

Put option – buy (long put)

Put option – sell (write) (short put)

Fall

Rise

Fall

Rise

Fall

Rise

Fall

Rise

Loss: premium only

Profit: unlimited

Gain: premium only

Loss: unlimited

Profit: unlimited

Loss: premium only

Loss: unlimited*

Gain: premium only

Note: these profiles only apply if strike price = price of underlying on deal day.

* = unlimited up to the point where the underlying has no value.

These payoff/loss profiles may be depicted as follows, but first we provide the assumptions:

Underlying commodity = platinum

Contract = 100 ounces

Strike price = see diagrams below

Premium (option price) = USD 10 per ounce (i.e. total of USD 1 000)

Option type = European.

Call option: buy (long call) at expiry

The long call option is depicted in Figure 5.349. If the price of platinum remains at USD 450 (per ounce50) or

falls below USD 450 for the term of the option contract, the buyer will not exercise the option, because it is

not profitable to do so. The option will lapse, and the buyer loses the premium amount USD 10 per ounce,

i.e. R1 000 (USD 10 x 100). He cannot lose more than this amount.

If the price moves upwards to say USD 455 at the end of the life of the option, the holder will exercise the

option because he will recover part of the premium paid, i.e. USD 500 (USD 5 x 100). The total loss of the

holder of the option will be half the premium, i.e. USD 500.

49 Note that in the figures the platinum price is per ounce and therefore profits / losses are per ounce.

50 All prices quoted hereafter are “per ounce”.

134

It should be clear that the exercising of the option means that the writer delivers 100 ounces of platinum to

the buyer for which the buyer pays USD 450 x 100 = USD 45 000. The total cost to the buyer / holder of the

option now is USD 46 000 (USD 45 000 plus the USD 1 000 premium). The buyer / holder of the platinum

now sells the platinum in the spot market at the spot market price of USD 455 and receives USD 45 500 (USD

455 x 100). The total loss is USD 500 (USD 46 000 – USD 45 500). If the holder does not exercise the option

the loss is R1 000 (the premium).

Figure 5.3: long call option

profit $

loss $

450 460 470

platinum price ($) at maturity

ATM

strikeprice

-10

+10

OTMITM

There are two other “options” for the buyer / holder in this regard:

• The holder could sell the option contract in the secondary market that exists for this paper. The

value of the contract will be close to the market price of the underlying asset (pricing is discussed in

some detail below).

• If the market is cash settled and the holder exercises, the writer pays the relevant amount to the

holder (i.e. USD 500), and the writer’s profit is USD 500.

If the spot platinum price moves to USD 460 (i.e. the strike price plus the premium) at the end of the life of

the option, it also pays the holder to exercise the option because he will recover the premium paid. The

option holder pays the writer USD 450 x 100 = USD 45 000, and sells the 100 ounces at the spot price of USD

460, i.e. for USD 460 x 100 = USD 46 000. The difference is USD 1 000 (USD 46 000 – USD 45 000), which is

equal to the premium paid.

At any price above USD 460, there are 3 possibilities (that apply every day until expiry):

• Exercise the option.

• Sell the option.

• Keep the option (to expiry and exercise on expiry).

135

It will be apparent that the profit potential of the holder is unlimited. If say the platinum price moves to USD

600 and the holder exercises, the profit is:

Amount paid = 100 x USD 450 = USD 45 000

Premium paid = 100 x USD 10 = USD 1 000

Total cost = USD 46 000

Amount sold for = 100 x USD 600 = USD 60 000

Profit = USD 60 000 – USD 46 000 = USD 14 000.

Figure 5.4: short call option

profit $

loss $

450 460 470


strikeprice

-10

+10

Call option: sell (write) (short call) at expiry

The short call option payoff profile is depicted in Figure 5.4.

The payoff profile of the seller/writer of the call option is the reverse of that of the buyer. The maximum the

seller can earn is USD 1 000, and the loss potential is unlimited. Thus, if the price at expiry is USD 450 or

lower, he makes a profit of USD 1 000. At USD 460, the writer makes nothing, and at any price above USD

460, the writer makes a loss.

Some of the jargon referred to earlier is pertinent here. An uncovered or naked short call is where the writer

does not have a position in the underlying instrument, i.e. is not holding the underlying instrument in

portfolio (in this case 100 ounces of platinum). Where the writer does have a matching position in the

underlying asset, he is covered, i.e. has a covered short call.

Put option: buy (long put) at expiry

The long put option payoff profile is depicted in Figure 5.5.

136

Figure 5.5: long put option

profit $

loss $

450 460 470


ATM

strikeprice

-10

+10

OTMITM

A put option is where the buyer has the right to “put” (sell to) the writer the underlying asset at a pre-

specified price. In this example, the strike price is USD 470, and the buyer pays a premium of USD 1 000

(remember, USD 10 per ounce).

This is the mirror image of buying a call, i.e. the buyer is hoping for a fall in the price to make a profit. At a

spot price of USD 470 or higher the buyer will allow the put option to lapse. At USD 460, the buyer breaks

even and he will exercise the option before or at expiry in order to break even. At any price lower than USD

460 the buyer will make a profit.

Put option: sell (write) (short put) at expiry

The short put option payoff profile is depicted in Figure 5.6.

At a spot platinum price of USD 470 or higher, the writer of a put option with a strike price of USD 470 will

make a profit of USD 1 000 (i.e. the premium). At say USD 465 the profit will be halved because the buyer

will exercise at expiry date). At any platinum price lower than USD 460, the writer’s potential loss is

unlimited (up to point where platinum price = 0).

137

Figure 5.6: short put option

profit $

loss $

450 460 470


strikeprice

-10

+10

5.5 INTRINSIC VALUE AND TIME VALUE

5.5.1 Introduction

The price or premium (P) of an option has two parts, i.e.:

• Intrinsic value (IV)

• Time value (TV).

Therefore:

P = IV + TV.

5.5.2 Intrinsic value

The difference between the spot price of the underlying asset (SP) and the exercise price of the option (EP) is

termed the intrinsic value (IV) of the option.

As seen, there are 3 categories in this regard:

• In-the-money (ITM) options (have an intrinsic value)

• At-the-money (ATM) options (have no intrinsic value)

• Out-the-money (OTM) options (have no intrinsic value).

ITM options are:

• Call options where: SP > EP

• Put options where: SP < EP.

138

Clearly, the following options have no intrinsic value (OTM):

• Call options where: SP < EP

• Put options where: SP > EP

• Call options where: SP = EP

• Put options where: SP = EP.

Thus:

IV = SP – EP (call options); positive when SP > EP

IV = EP – SP (put options); positive when EP > SP.

A summary is provided in Table 5.2.

TABLE 5.2: PAYOFF PROFILES: ITM, ATM AND OTM OPTIONS

ITM / ATM / OTM Call options Put options

ITM SP > EP IV > 0 SP < EP IV > 0

ATM SP = EP IV = 0 SP = EP IV = 0

OTM SP < EP IV = 0 SP > EP IV = 0

5.5.3 Time value

The time value (TV) of an option is the difference between the premium (P) of an option and its intrinsic

value (IV):

P = IV + TV

TV = P – IV.

An example is required:

Option = call option

Underlying asset = ABC share

Underlying asset spot market price (SP) = R70

Option exercise price (EP) = R60

Intrinsic value (IV) = SP – EP = IV = R70 – R60 = R10

Premium (P) = R12

Time value (TV) = P – IV = TV = R12 – R10 = R2.

139

The option has time value of R2, and this indicates that there is a probability that the intrinsic value could

increase between the time of the purchase and the expiration date. If the option is exercised now (i.e. at

R60), the intrinsic value is gained, but time value is forgone. It will be apparent that as an option moves

towards the expiration date, time value diminishes, and that at expiration time value is zero. This is

portrayed in Figure 5.7.

timevalue

days to expiry 0 days

Figure 5.7: time value of option

5.6 OPTION VALUATION/PRICING


THE STUDENT IS NOT EXPECTED TO CALCULATE OPTION VALUES APPLYING ANY PRICING MODEL

5.6.1 Introduction

There are two main option pricing / valuation models that are used by market participants:

• Black-Scholes model.

• Binomial model.

Below we also mention the other pricing models and define the so-called "Greeks".

5.6.2 Black-Scholes model

The Black-Scholes model was first published in 1973 and essentially holds that the fair option price (or

premium) is a function of the probability distribution of the underlying asset price at expiry. It has as its main

constituents the following (see the valuation formula below)51:

51 This section relies heavily on Hull (2000: 250).

140

• Spot (current) price of underlying asset (assume share) (SP).

• Exercise (strike) price (EP).

• Time to expiration.

• Risk free rate (i.e. treasury bill rate).

• Dividends expected on the underlying asset during the life of the option.

• Volatility of the underlying asset (share) price.

Each of these elements is covered briefly below.

Spot (current) price of underlying asset and exercise price

If a call option is exercised the profit is:

SP – EP (obviously if SP < EP, there is no profit).

Call options are therefore more valuable as the SP of the underlying asset increases (EP a given) and less

valuable the higher EP is (SP a given). The opposite applies in the case of put options. The profit on a put

option if exercised is:

EP – SP (obviously if EP < SP there is no profit).

Put options are therefore more valuable as the SP of the underlying asset decreases (EP a given) and less

valuable the lower EP is (SP a given).

Time to expiration

The longer the time to expiration the more valuable both call and put options are. The holder of a short-term

option has certain exercise opportunities. The holder of a similar long-term option also has these

opportunities and more. Therefore the long option must be at least equal in value to a short-term option

with similar characteristics. As noted above, the longer the time to expiration the higher the probability that

the price of the underlying assets will increase/decrease.

Risk free rate

The risk free rate (rfr) is the rate on government securities. The effect of the rfr on option prices is not as

clear-cut as one would expect. As the economy expands, rates tend to increase, but so does the expected

rate of share price increases, because dividends increase. It is also known that the present value of future

cash flows also decreases as rates increase.

These two effects tend to reduce the prices of put options, i.e. the value of put options decreases as the rfr

increases. However, it has been shown that the value of call options increase as the rfr increases, as the

former effect tends to dominate the latter effect.

Dividends

Dividends have the effect of reducing the share price on the ex-dividend date. This is positive for puts and

negative for calls. The size of the expected dividend is important, and the value of call options is therefore

negatively related to the size of the expected dividend. The opposite applies to put options.

141

Volatility

Of these factors, the only one that is not observable is volatility, i.e. the extent of variance in the underlying

asset price. This is estimated (calculated) from data in the immediate past.

It will be clear that as volatility increases, so does the chance that the share will do well or badly. The

investor in a share will not be affected because these two outcomes offset one another over time. However,

in the case of an option holder the situation is different:

• The call option holder benefits as prices increase and has limited downsize risk if prices fall.

• The put option holder benefits as prices decrease and has limited downsize risk if prices rise.

Thus, both puts and calls increase in value as volatility increases.

The model

The Black-Scholes valuation model is as follows (European call option):

Pc = N(d1)S0 – E(e-rt

)N(d2)

where

Pc = price of European call option

S0 = price of the underlying asset currently

E = exercise price of the option

e = base of the natural logarithm, or the exponential function

r = risk-free rate per annum with maturity at expiration date

N(d) = value of the cumulative normal distribution evaluated at d1 and d2

t = time to expiry in years (short-term = fraction of a year)

d1 = [ln(S0/E) + (r + σ2/2)t] / σ t

d2 = d1 - σ t

ln = natural logarithm (Naperian constant = 2.718)

σ2 = variance (of price of underlying asset on annual basis)

σ = standard deviation (of price of underlying asset on annual basis).

In the case of a European put option, the price formula changes to:

Pp = – E(e-rt

)N(–d2) – N(–d1)S0.

142

The one parameter of the model that cannot be directly observed is the price volatility of the underlying

asset (standard deviation). It is a measure of the uncertainty in respect of returns on the asset. According to

research, typically, volatility tends to be in the range of 20 – 40% pa. This can be estimated from the history

of the assets. An alternative approach is implied volatility, which is the volatility implied by the option price

observed in the market.52

Implied volatilities are used to gauge the opinion of market participants about the volatility of a particular

underlying asset. Implied volatilities are derived from actively traded options and are used to make

comparisons of option prices.

The Black-Scholes option pricing model is not the Midas formula, because it rests on a number of simplifying

assumptions such as the underlying asset pays no interest or dividends during its life, the risk-free rate is

fixed for the life of the option, the financial markets are efficient and transactions costs are zero, etc.

However, it is very useful in the case of certain options (see section on binomial model after the following

section). Next we present an example.

5.6.3 Example of Black-Scholes option pricing

The underlying asset is a non-dividend-paying share of company XYZ the current share price of which is

R100. The option is a European call, its exercise price is R100 and it has a year to expiry. The risk-free rate is

6.0% pa, historical volatility is 30% and the standard deviation of the share’s returns is 0.1 per year. Thus:

S0 = R100

E = R100

r = 0.06

t = 1

σ2 = 0.01

σ = 0.1

d1 = [1n(S0/E) + (r + σ2/2)t] / σ t

= [1n(100/100) + (0.06 + 0.005)1] / 0.1 1

= 0.065 / 0.1

= 0.65.

From the cumulative normal distribution table53 one can establish the value of N(d1):

N(d1) = N(0.65) = 0.7422.

Similarly we find the value of N(d2):

52 See Hull (2000: 255).

53 Not supplied here.

143

d2 = d1 - σ t

= 0.65 – 0.1

= 0.55

N(d2) = (0.55) = 0.7088 (from table).

We are now able to complete the model:

Pc = N(d1)S0 – E(e-rt)N(d2)

= (0.7422 x R100) – (R100 x 2.718-0.06x1 x 0.7088)

= R74.22 – (R100 x 0.94177 x 0.7088)

= R74.22 – R66.75

= R7.47.

5.6.4 Binomial model

The Black-Scholes model is regarded as a good valuation model for certain options, particularly for European

options on commodities. However, it is regarded as less accurate for dividend paying options and particularly

so if the option is of the American variety. Also, it tends to undervalue deep-in-the-money options. Another

problem is the assumption of log normality of future asset prices.

Where the Black-Scholes is regarded as weak, the binomial model is used. This model involves the

construction of a binomial tree, i.e. a diagram representing different possible paths that may be followed by

the underlying asset over the life of the option.

5.6.5 Other models

In addition to these two valuation models, there is another two:

• Monte Carlo simulation.

• Finite difference methods (implicit finite difference method and explicit finite difference method).

5.6.6 The Greeks

In the derivative markets reference is often made to the Greek letters, known as the "Greeks". The "Greeks"

measure different dimensions of risk in option positions as follows:54

Delta

The delta is the rate of change of the option price with respect to the price of the underlying asset.

54 This section draws heavily from Hull (2000).

144

Theta

The theta of a portfolio of derivatives is the rate of change of the portfolio value with respect to the passage

of time (ceteris paribus - when all else remains the same). It is often referred to as the time decay of the

portfolio.

Gamma

The gamma of a portfolio of derivatives on an underlying asset is the rate of change of the portfolio's delta

with respect to the price of the underlying asset.

Vega

The vega of a portfolio of derivatives is the rate of change of the value of the portfolio with respect to the

volatility of the underlying asset.

Rho

The rho of a portfolio of derivatives is the rate of change of the portfolio value with respect to the interest

rate.

5.7 ORGANISATIONAL STRUCTURE OF OPTION MARKETS

One way of depicting the organisational structure of option markets is as in Figure 5.8.

The market form of options is a mixture of formal in the shape of an exchange where options are listed, and

OTC. There are many futures / options exchanges in the world, or futures / options divisions of exchanges as

in the case of South Africa. There are also substantial OTC markets.

As to whether option markets are primary markets and/or secondary markets, the answer depends on

whether they are OTC or exchange-traded. In the case of the OTC markets, there are primary markets in

which options are issued and secondary markets in which existing options can be sold and bought. In the

case of exchange-traded options the primary and secondary markets are “merged”. They are issued by the

exchange (primary market) and can be “sold” (“closed out”) in the sense of dealing in the opposite direction.

For example, if a client has a call option, she can close out the position by buying a put. The “closing out”

results in a loss or profit as in the case of a spot instrument sale in the secondary market.

The main advantage of exchange-traded options is that they are guaranteed by the exchange, they are

standardised and they are (usually) liquid markets. The main advantage of the OTC market is that the

options are customised. The differences between these two markets are as shown in Table 5.3.

145

market nature

PRIMARY MARKET

market form

market type

trading driver

trading system


trading form

ORDER QUOTE

OTC EXCHANGE

FLOOR TEL / SCREEN

ATSSCREEN / TEL

SINGLE CAPACITY

DUAL CAPACITY

Figure 5.8: organisation of options markets

SECONDARY MARKET

OTC

QUOTE

TEL / SCREEN

TABLE 5.3: COMPARISON OF OTC AND FORMALISED OPTIONS MARKETS

OTC Exchange-traded

Regulation None Yes

Contracts

Usually not standardised

(standardised in certain

respects)

Standardised

Margin Sometimes Yes

Delivery dates Customised (large range) Standardised (limited range)

Delivery of underlying

instrument Almost always Few settled by delivery

Instruments Virtually all Virtually all

Secondary market

tradability Limited Liquid secondary markets

Participants Large players only Large and small players

Risk Deal between counterparties

– each faces risk Contracts guaranteed by exchange

Market Screen or telephone or both Open outcry on exchange floor, or telephone or

ATS

146

The trading-driver process of listed options is the same as in the case of listed futures. The client telephones

the broker and places an order to sell or buy a particular number of call or put options. She will of course

also state the expiration date/s and strike price/s. The order placed is either a market order or a limit order.

The former is an instruction to deal at the best available price, while the latter is an order to transact at a

specific price.

In the case of the South African listed options market this information will be inputted into the ATS system

and left there until a match is found (which in most markets is usually a few seconds or minutes because

these markets are so liquid). In the case of an open outcry system of trading (as in certain overseas markets),

the order is communicated to the trader in the pit. Traders form groups reflecting the various delivery dates.

The order is “cried out” and another trader “cries out” if she has an opposite matching order. The trade is

done with a floor broker, a market maker or a professional trader.

In OTC markets the method of trading is screen / telephone (as in the case of South Africa) or just telephone,

and the trading driver is quote. Certain broker-dealers quote option buying and selling prices (premiums).

Settlement takes place on T+1 or T+2.

It will be apparent that not just anyone is able to trade in the OTC market, and this is because each party is

directly exposed to the other party in terms of risks such as settlement risk, risk of tainted scrip, default risk,

etc. One needs credentials and a track record to deal in the OTC options markets.

5.8 OPTIONS ON DERIVATIVES: FUTURES



5.8.1 Introduction

The options market overview illustration is reproduced here for the sake of orientation (see Figure 5.9).

OPTIONS

debt market

forexmarket


marketbond market

equity market




Figure 5.9: options

As noted, all futures markets are formalised markets. Options are available on virtually all futures, and most

of these options are exchange-traded. The word “most” is used here because in some markets OTC options

on futures also exists.

147

• A long position in the underlying futures contract.

• Plus an amount that is equal to the difference between the last MTM55 futures price and the

exercise price (futures price - exercise price).

Conversely, when the holder of a put on a future exercises the option, the writer is obligated to deliver to the

holder of the put:

• A short position in the underlying futures contract.

• Plus an amount that is equal to the difference between the exercise price and the last MTM futures

price (exercise price - futures price).

In practice, however, most options on futures are settled in cash. It will be recalled that the futures market

may be categorised (with examples included) as shown in Table 5.4

As noted, options are available on virtually all futures. In the US the most active options on futures contracts

are the options on treasury bond futures and treasury note futures, options on the Eurodollar futures, and

options on the futures contracts on corn, soybeans, and crude oil.

In South Africa, options are available on virtually all the futures contracts that are listed. Table 5.5 serves as a

reminder.

TABLE 5.4: EXAMPLES OF FUTURES CONTRACTS



Physical

Treasury bonds

Treasury notes

Treasury bills

Federal funds

Canadian govt bond

Eurodollar

Euromark

Euroyen

Eurobond

Index (notional)

Short sterling bond index

Long sterling bond index

Municipal bond index

Physical

Various specific

shares

Index (notional)

DJ Industrial

S&P 500

NASDAQ 100

CAC-40

DAX-30

FTSE 100

Toronto 35

Nikkei 225

NYSE

Physical

Japanese yen

DM

British pound

Swiss franc

French franc

Australian dollar

Brazilian real

Mexican peso

Sterling/mark cross

rate

Index (notional)

US dollar index

Grains and oilseeds

Wheat

Soybeans

Corn (maize)

Livestock and meat

Cattle – live

Hogs – lean

Pork bellies

Food and fiber

Cocoa

Coffee

Sugar

Cotton

Orange juice

Physical - Metals

Gold

Platinum

Silver

Copper

Aluminium

Palladium

Physical -Energy

Crude oil light sweet

Natural gas

Brent crude

Propane

Index (notional)

CRB index

Physical = the actual instrument, currency, commodity. Index = indices of exchanges, etc. CRB index = Commodity Research Bureau.

55 Last mark to market price. In this regard see Hull (2000:285).

148

TABLE 5.5: SELECTION OF SOUTH AFRICAN FUTURES CONTRACTS


Interest rate Equity Foreign

currencies Agricultural

Metals and

energy

Physical

Futures on:

R186 long bond (10.5%

2026)

R194 long bond

(10.0% 2008)

R201 long bond

(8.75% 2014)

3-month JIBAR interest rate

Notional swaps (j-Notes)

FRAs (j-FRAs)

Index (notional)

Futures on:

ALBI index (j-ALBI)

GOVI index(j-GOVI)

Physical

Futures on:

+ / - 200 shares (called

single stock futures –

SSFs)

Dividends (local &

foreign)

Index (notional)

Futures on:

FTSE/JSE Top 40

FTSE/JSE INDI 25

FTSE/JSE FINI 15

FTSE/JSE FNDI 30

FTSE/JSE RESI 20

FTSE/JSE African banks

FTSE/JSE gold mining

Physical

USD/ZAR

EUR/ZAR

GBP/ZAR

AUD/ZAR

Index

(notional)

None

Physical

Local:

White maize

Yellow maize

Soybeans

Wheat

Sunflower seed

Foreign (underlying

= foreign futures)

Corn

Index (notional)

None

Physical

Local:

Kruger Rand

Foreign

(underlying =

foreign futures)

Gold

Platinum

Crude oil

Index (notional)

None

It may be useful to provide an example of an option on futures deal:

5.8.2 Example

An investor requiring a general equity exposure to the extent of R1 million decides to acquire this exposure

through the purchase of call options on the ALSI future. If the index is currently recorded at 5 000, she would

require 20 call option contracts (20 x R10 x 5000 = R1 000 000) (remember that one ALSI futures contract is

equal to R10 times the index value).

Because the investor is buying the right to purchase the future and has no obligation in this regard, she pays

a premium to the writer. In this example we make the assumption that the premium is R1 500 per contract

(R30 000 for 20 contracts). The investor is thus paying R30 000 for the right to purchase 20 ALSI futures

contracts at an exercise or strike price of 5000 on or before the expiry date of the options contract.

It will be evident that the premium per contract of R1 500 translates into 150 points in the all share index (R1

500 / R10 per point). Thus, the investor’s breakeven price is 5150 (5000 + 150). This can be depicted as the

plum-coloured line in the payoff diagram shown in Figure 5.10.

149

profit

lossstrikeprice

5150

-R1 500

+R1500

holder(buyer)

writer

ALSI index value at maturity

5 000 5300

0

Figure 5.10: payoff profile of writer and holder of call option

Assuming that the buyer (investor) holds the contracts to expiry:

• If the price closes at or below 5000 she will not exercise. She incurs a loss equal to the premium

paid, i.e. R1 500 per contract.

• If the price closes between 5000 and 5150 she will exercise the options and recover a portion of the

premium.

• If the market closes at a price above 5150 she will exercise and make a profit. For example, if the

price at expiry is 5400, her profit is R2 500 per contract [i.e. R10 x (5400 - 5150)].

The risk profile of the writer is exactly the reverse of that of the holder. As can be seen in Figure 5.10:

• The writer makes a profit of R1 500 (the premium) per contract if the price closes at or below 5000.

• The writer makes a profit of less than R1 500 per contract if the price closes at between 5000 and

5150. This is because the holder will exercise between these two prices in order to recover a portion

of her premium.

• The writer makes a loss if the price rises above 5150. For example, if the price closes at 5600, the

writer will make a loss of R4 500 [R10 x (5600 - 5150)] per contract.

It will be apparent that the investor gained her R1 million exposure with a monetary outlay of R30 000. Thus,

she is able to invest the balance of R970 000 in the money market and receive the current interest rate.

The money market rate (rfr) is thus an important input in the pricing of options (as seen above).

150

The buyer of a put option has a risk profile which is the converse of that represented by a call option (see

Figure 5.11). For example, an investor wanting to hedge his R1 million equity exposure (i.e. anticipating that

share prices will fall) would buy 20 put option contracts on the ALSI future (assuming the strike price to be

5000). She is thus hedged to the extent of R10 x 20 x 5000 = R1 000 000. She thus has the right, but not the

obligation, to sell to the writer (seller) 20 ALSI futures contracts on or before the expiry date of the options

contracts. Assuming that the premium paid is R1 500 per contract, her risk profile is as depicted in Figure

5.11.

As far as the holder is concerned:

• If the price closes at 5000 or higher, she will not exercise and the loss is limited to R1 500 per

contract.

• If the price closes at between 5000 and 4850, she will exercise and recover a portion of the

premium.

• If the price falls below 4850 she makes a profit equal to R10 per point per contract.

Conversely, the writer of the put options will profit to the extent of R1 500 per contract if the price at close is

5000 or better, profit less than R1 500 at a price between 4850 and 5000 and incur a loss at a price below

4850 to the extent of R10 per point per contract.

Options on futures are also subject to margin requirements. These are the same as for the underlying

futures.

profit

lossstrikeprice

5130

-R1 500

+R1500

holder(buyer)

writer

ALSI index value at maturity

50004850

0

4700

Figure 5.11: payoff profile of writer and holder of put option

151

5.8.3 Option specifications

As will be understood, options contracts take on many of the features of the underlying instruments, i.e. the

futures contracts. The below-mentioned option specifications should therefore be read together with the

futures contract specifications (see Table 5.6).

TABLE 5.6: OPTION SPECIFICATIONS

Expiry The same time and date as the underlying futures contract

Style American

Types Both a call and a put at each strike (exercise)

Strike price units Strike prices are specified in the units of quotation of the underlying futures contract

Strike price intervals Strike prices are at fixed intervals.

Live strikes Three strike prices are “live”, i.e. are accommodated on the screens. The corresponding options are

“at”, “in” and “out” of the money, and are referred to as “strike 1”, “strike 2” and “strike 3” on the

screens. A separate screen gives the value of the strike price associated with each of the three.

Strike shifts The live strikes are shifted, and new strikes introduced (if necessary) whenever the underlying financial

instrument’s price:

• Moves beyond either of the away-from-the-money strikes or

• Is consistently closer to an away-from-the-money strike than to the at-the-money strike for

one trading day.

Shifts are not normally more frequent than daily, and are made overnight. All shifts are made at the

exchange’s discretion.

Free-format screens Quotations for options whose strike prices are not live are entered onto one or more free-format

screens

Contract size Each option is on one contract of its underlying financial instrument

Standard lot size (Number of options that quotations are good for). The same as the underlying financial instrument’s

standard lot size.

Quotations Quotations are in whole rands per option

Settlement of premiums Through the mark to market process over the life of the option

Mark-to-market Daily according to the option’s mark to market price (i.e. the same as for futures)

Determination of

mark to market prices

• Quoted doubles are used where available

• Implied volatilities are calculated from available prices to value options (on the same

underlying financial instrument) lacking quotes

• Exchange has the discretion to override the former and to specify volatilities overriding the

latter

Exercise May be exercised at any time until expiry. A client’s option is exercised through his member directly

with the exchange

Settlement on exercise Into the underlying financial instrument

Assignment Options exercised will be randomly assigned to short positions in the same option. Assigned holders (or

their members), and their clearing members, will be notified immediately. Assignment will be in

standard lot sizes as far as possible.

Automatic exercise All in-the-money options will be automatically exercised (into the underlying financial instrument) on

expiry. This happens before the close out by the exchange of positions in futures contracts.

Marns Option positions are subject to the same initial margin requirements as their underlying financial

instruments. However, the potential profit/loss profile of options is recognised. Margins are also

affected by volatility margin requirements.

Source: Safex / JSE.

152

The two basic uses of options on futures are to protect a future investment’s return from falling interest

rates / rising prices (call option), and to protect against rising interest rates / falling prices (put options).

5.8.4 Turnover in options on futures in South Africa

The turnover in options on futures in South Africa is shown in Table 5.7. The numbers are impressive: the

average number of contracts turned over per day in 2001 was 97 662, at an average value of R480 million.

TABLE 5.7: TURNOVER: OPTIONS ON FUTURES CONTRACTS

Year Number of deals Number of

contracts

Underlying value

(R millions) Open interest

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

17 938

17 117

18 870

11 731

13 130

19 701

12 818

11 335

11 299

12 473

16 534

21 137

23 723

5 199 938

6 437 214

8 726 702

9 618 066

15 044 477

24 317 784

19 120 789

17 404 419

18 136 543

14 410 203

17 552 862

30 455 493

37 804 393

12 190

19 038

37 278

32 767

60 007

119 416

78 316

50 127

49 808

49 854

96 656

102 867

179 273

687 594

1 036 058

1 252 635

1 433 644

2 378 928

2 556 934

3 002 783

2 414 355

2 145 487

2 076 788

2 260 074

5 909 619

5 387 259

Source: South African Reserve Bank Quarterly Bulletin. Open interest = outstanding contracts at the end of each day.

5.9 OPTIONS ON DERIVATIVES: SWAPS



Figure 5.12 is presented here for the sake of orientation. We discussed swaps in some detail in the previous

chapter. An option on this derivative is the option on the swap, called the swaption.

We saw earlier that there are four types of swaps that relate to the financial markets and the commodity

market (see Figure 5.13). We also saw that there exists a forward swap (or deferred swap) (it is mentioned

here again because it is touched upon below).

153

OPTIONS

debt market

forexmarket


marketbond market

equity market




Figure 5.12: options

Options are not found on all these swaps, but only on the interest rate swap, i.e. a swaption is a combination

of an interest rate swap and an option. As elucidated above, in interest rate swaps, fixed-rate obligations

(cash flows) are swapped for floating rate obligations. In swaptions, the underlying instrument is the fixed-

rate obligation. Thus, a call swaption imparts the right to the holder to receive the fixed rate in exchange for

the floating rate, while in put swaptions, the holder has the right to pay fixed and receive floating.

FINANCIAL AND COMMODITY SWAPS

INTEREST RATE SWAPS

debt market

forexmarket


marketbond market

equity market

CURRENCY SWAPS

COMMODITY SWAPS

EQUITY SWAPS

FINANCIAL MARKETS

Figure 5.13: swaps

154

An example may be useful.56 A company knows that in six months’ time it is to enter into a five-year floating

rate loan (i.e. borrowing) agreement at 3-month JIBAR, and wants to swap the floating rate payments into

fixed rate payments, i.e. to convert the loan into a fixed rate loan (because the company believes that rates

are about to rise).

For a premium, the company can buy a (put) swaption from a broker-dealer in this type of paper. The

swaption gives the company the right to receive the 3-month JIBAR rate on a notional amount that is equal

to its loan, and to pay a fixed rate of interest every three months at 14% pa (assumed) for the next five

years, starting in six months’ time. The “options” the company has are clear:

If in six months time the fixed rate on a normal 5-year swap is lower than 14%, the company will allow the

swaption to lapse (remember the company wants to pay fixed)

The company will then undertake a normal interest rate swap at the lower fixed rate (the floating rate will

probably still be 3-month JIBAR)

If the fixed rate on normal swaps is higher than 14%, the holder will exercise the swap and take up the swap.

The company is guaranteed that the fixed rate it will pay on the future will not exceed an agreed fixed rate.

Thus the company has protection against rates moving up, while retaining the option to benefit from lower

rates in the future.

The swaption is an alternative to the forward swap. The latter obliges the holder to enter into a swap after a

stipulated period, but the holder pays no premium for it. In the case of the swaption, the holder is not

obligated and can allow the swaption to lapse, i.e. it allows the holder to benefit from favourable interest

rate movements.57

5.10 OPTIONS ON DEBT MARKET INSTRUMENTS


DEFINITIONS ONLY IN THIS SECTION (5.10) WILL BE EXAMINED

5.10.1 Introduction

The options market illustration presented here again is designed to orientate the reader in terms of the

place of the market being discussed (see Figure 5.14).

The term “debt market instruments” in respect of options encompasses money and bond market specific

instruments (“physicals”) (or rather some of them) and notional instruments (indices) (or some of them).

They may be classified as follows:

56 With assistance from Hull (2000:.543).

57 The swaption-swap differences are similar to the differences between an option on forex and a forex forward. See Hull (2000:

543).

155

Money market options:

• Options on specific money market instruments

• Interest rate caps and floors.

Bond market options:

• Options on specific bonds

• Options on bond indices

• Bond warrants (retail options)

• Bond warrants (call options)

• Callable and puttable bonds (bonds with embedded options)

• Convertible bonds.

OPTIONS

debt market

forexmarket


marketbond market

equity market





Money market options are comprised of options on specific money market instruments (and this includes

ordinary deposits) and caps and floors (these are option-like instruments). As seen in the list, there are a

number of bond option varieties. The first three mentioned above are full-blooded bond options, while the

latter three may be termed option-like securities in the bond market. We discuss all these a little later.

Options on bond futures are obviously not discussed in this section (they were discussed under “options on

derivatives”).

5.10.2 Options on specific money market instruments

Money market options are options that are written on specific money market instruments, such as

commercial paper, NCDs, deposits, etc. Not many countries have specific asset money market options,

because of the existence of the active markets in other money market derivatives (swaps, swaptions, repos,

caps and floors, FRAs, and interest rate futures).

156

Some countries, however, have options on notional money market instruments. A UK example is presented

in Table 5.8.58

TABLE 5.8: EXAMPLE OF OPTION ON MONEY MARKET INSTRUMENT

LIFFE SHORT STERLING OPTION GBP 500 000, POINTS OF 100%

Strike price Calls Puts

Dec Mar Jun Dec Mar Jun

9350 0.11 0.08 0.09 0.06 0.33 0.66

9375 0.01 0.02 0.04 0.21 0.52 0.86

9400 0.00 0.01 0.02 0.45 0.76 1.09

Let us focus in on the June call option at a strike (exercise) price of 9350, and a premium of 0.09. What do

these numbers mean? The holder of the option has the right to make a deposit of GBP 500 000 on the expiry

date in June (the date is specified) at an interest rate of 6.5% (100 – 93.50) for 3 months. Each tick

movement on the contract, which is equivalent to one basis point, is worth the value of the contract (GBP

500 000) multiplied by 1 basis point (0.01% or 0.0001) and a quarter of a year (0.25), i.e.:

GBP 500 000 x 0.0001 x 0.25 = GBP 12.50.

The cost of the call option (i.e. the premium), is therefore 9 x GBP 12.50 = GBP 112.50.

If by the expiry date the contract strike price rises to 9450 (interest rates have fallen to 5.5%) the holder is

entitled to a gain of 100 basis points, and the profit is 100 x GBP 12.50 = GBP 1 250.00 less the premium of

GBP 112.50 = GBP 1 137.50.

On the other hand, if interest rates have risen (to 7% pa) so that the contract is trading at 9300, the contract

will not be exercised and the holder will forego the premium of GBP 112.50.

5.10.3 Caps and floors

Description

Caps and floors (a combination of which is termed a collar) are akin to options. In fact they are so similar to

options that they could be termed cap options and floor options. Because of their option-like attributes, they

are placed in this chapter on options.

A cap purchased makes it possible for a company with a borrowing requirement to hedge itself against rising

interest rates. The cap contract establishes a ceiling, but the company retains the right to benefit from falling

interest rates. On the other hand, a floor contract allows a company with an investment requirement (surplus

funds) to shield itself against declining interest rates by determining a specified floor upfront, while it retains

the right to profit from rising interest rates.

58 Example (slightly) adapted from Pilbeam, 1998.

157

On the exercise date of the cap or floor contract, the specified strike rate is evaluated against the standard

reference rate (i.e. usually the equivalent-term JIBAR rate). The interest differential is then applied to the

notional principal amount that is specified in the contract, and the difference is paid by the seller/writer to

the buyer/holder. The buyer of a floor or cap pays a premium for the contract, as in the case of an option or

insurance policy.

Caps

deal date(3-M JIBAR rate = 10.3%)

settlement date(3-M JIBAR rate = 11.2%)

time line

cap strike rate= 10.5%

DAY 0

1 MONTH

2 MONTHS

3 MONTHS

4 MONTHS

5 MONTHS

6 MONTHS

Figure 5.15: example of T3-month – T6-month cap

It is perhaps best to elucidate a cap with the assistance of an example: borrowing company buys a T3-month

– T6-month cap (see Figure 5.15).

A company needs to borrow R20 million in 3 months’ time for a period of 3 months, and is concerned that

interest rates are about to rise sharply. The present 3-month market rate (JIBAR rate = market rate) is 10.3%

pa. The company is quoted a T3-month – T6-month (T3m-T6m) cap by the dealing bank at 10.5%, i.e. the 3-

month JIBAR borrowing rate for the company is fixed 3-months ahead. The company accepts the quote and

pays the premium of R25 000 to the dealing bank. The number of days of the period for which the rate is

fixed is 91.

If the JIBAR rate (= market rate on commercial paper, the borrower’s borrowing habitat) in 3-months’ time

(i.e. settlement date), is 9.3%, the company will allow the cap to lapse (i.e. will not exercise the cap) and

instead will borrow in the market at this rate by issuing 91-day commercial paper. The total cost to the

company will be the 9.3% interest plus the premium paid for the cap:

Cost to company = (C x ir x t) + P

where

C = consideration (amount borrowed)

ir = interest rate (expressed as a unit of 1)


P = premium

158

Cost to company = (C x ir x t) + P

= R20 000 000 x 0.093 x 91 / 365) + R25 000

= R463 726.03 + R25 000

= R488 726.03.

It will be apparent that the interest rate actually paid by the company (ignoring the fact that the premium is

paid upfront) is:

Total interest rate paid = R488 726.03 / R20 000 000 x 365 / 91

= 0.0244363 x 4.010989

= 0.09801

= 9.80% pa.

If the JIBAR rate on the settlement date is say 11.2% pa, settlement will take place with the dealing bank

according to the following formula:

SA = NA x [(rr – csr) x t]

where

SA = settlement amount

NA = notional amount

rr = reference rate

csr = cap strike rate


SA = R20 000 000 x [(0.112 – 0.105) x 91 / 365]

= R20 000 000 x (0.007 x 91 / 365)

= R34 904.11.

The financial benefit to the company is equal to the settlement amount minus the premium:

Financial benefit = SA – P

= R34 904.11 – R25 000

= R9 901.11.

The company thus borrows at the market rate of 11.2%, but this rate is reduced by the amount paid by the

bank to the company less the premium paid to the bank:

159

Cost to company = (C x ir x t) – (SA – P)

= (R20 000 000 x 0.112 x 91 / 365) – (R9 901.11)

= R558 465.75 – R9 901.11

= R548 564.64

Total interest rate paid = (R548 564.64 / R20 000 000) x (365 / 91)

= 0.0274282 x 4.010989

= 0.110001

= 11.00% pa.

This of course ignores the fact that the premium is paid up front.

Floors

It is useful to elucidate floors with the use of a specific example: investing company buys a T3-month – T6-

month floor (see Figure 5.16).

deal date(3-M JIBAR rate = 11.4%)

settlement date(3-M JIBAR rate = 10.4%)

time line

floor strike rate= 11%

DAY 0

1 MONTH

2 MONTHS

3 MONTHS

4 MONTHS

5 MONTHS

6 MONTHS

Figure 5.16: example of T3-month – T6-month floor

An investor expects to receive R20 million in 3 months’ time, and these funds will be free for 3 months

before it is required for a project. The investor expects rates to fall and would like to lock in a 3-month rate

now for the 3-month period (assume 91 days) in three months’ time. He approaches a dealing bank and

receives a quote for a T3m-T6m floor at 11.0% on a day when the 3-month market (JIBAR) rate is 11.4%. He

verifies this rate with other dealing banks, and decides to deal. The premium payable is R19 000.

Three months later (on the settlement date) the JIBAR 3-month rate is 10.4% pa. The investor was correct in

his view and the bank not, and the bank coughs up the following (fsr = floor strike rate):

160

SA = NA x [(fsr – rr) x t]

= R20 000 000 x [(0.11 – 0.104) x 91 / 365]

= R20 000 000 x (0.006 x 91 / 365)

= R20 000 000 x 0.00149589

= R29 917.81.

The financial benefit to the company is:

Financial benefit = SA – P

= R29 917.81 – R19 000

= R10 917.81.

The company thus invests at the 3-month cash (spot) market rate of 10.4% pa on the settlement date, and

its earnings are boosted by the settlement amount less the premium paid to the bank:

Earning on investment = (C x ir x t) + (SA – P)

= [R20 000 000 x (0.104 x 91 / 365)] + R10 917.81

= (R20 000 000 x 0.025929) = R10 917.81

= R518 575.34 + R10 917.81

= R529 493.15.

Thus, the actual rate (ignoring the fact that the premium is paid upfront) earned by the company is:

Total interest rate earned = (R529 493.15 / R20 000 000) x (365 / 91)

= 0.0264747 x 4.010989

= 0.1061897

= 10.62% pa.

It will be evident that if the spot market rate is say 11.5%, the treasurer of the investing company will let the

floor contract lapse (i.e. not exercise). He will invest at 11.5% for the 3-month period, but this return is

eroded by the premium paid for the floor. The following are the relevant numbers:

Earnings on investment = (C x ir x t) - P

= (R20 000 000 x 0.115 x 91 / 365) - R19 000

= R573 424.66 - R19 000

= R554 424.66.

It will be apparent that the interest rate actually earned by the company (ignoring the fact that the premium

is paid upfront) is:

161

Total interest rate earned = (R554 424.66 / R20 000 000) x (365 / 91)

= 0.0277212 x 4.010989

= 0.1118943

= 11.12% pa.

Thus, the investor would have been worse off if he had exercised the floor.

5.10.4 Options on specific bonds

Introduction

An option on a specific bond, also called a bond option, may be defined as an option to buy (call) or sell (put)

a specific bond on or before an expiry date at a pre-specified price or rate. “Price or rate” is mentioned

because some markets deal on price and some on rate; South Africa deals on a rate (ytm) basis.

Bond option markets are OTC and/or exchange-driven markets. In South Africa both are found.

OTC bond options

In the OTC options markets, the contracts are generally standardised (in most respects). Options are written

on the most marketable short- and long-term bonds, which are the high-capitalisation bonds.

The OTC bond options written and traded are of the standardised and American variety. European options

are also written from time to time, and there are also non-standardised options. The latter, which include

“overnighters” (i.e. contracts written to expire the following day), are usually written to suit particular

hedging strategies. They differ from the standardised contracts in terms of expiration date and strike rate

level.

The characteristics of standardised bond options are shown in Table 5.9.

TABLE 5.9: CHARACTERISTICS OF STANDARDISED BOND OPTIONS

Size of contract R1 million (nominal value), but the standard trading amount is R10 million or

multiples of this amount

Underlying instruments Various government and public enterprise bonds

Market price/rate Yield to maturity

Strike rate intervals 0.25%, for example 12.00%, 12.25%, 12.50%, 12.75%

Expiry dates 12 noon on the first Thursday of February, May, August and November

Commission As there are no fixed commission rates, the commission is included in the premium

paid by the purchaser

Form of settlement Cheque for the premium negotiated on the day of settlement

162

Listed bond options59

Exchange-traded options on specific bonds were listed on BESA (now part of the JSE) in the past. They were

European style options (call and put) on the most tradable bonds and they were physically settled. The

product specifications are shown in Table 5.10.

BESA provided an example in the past as follows:

“Consider a BOR194 Dec04C call option contract. This will trade on implied volatility and a strike price

corresponding to a yield level which will be specified by both parties involved in the trade.

“If on the maturity date, the option is in the money, physical delivery of the underlying will occur at the

strike level (or closed out for cash). Suppose a trade occurs for a single contract at a strike level of 9% and at

an implied volatility of 20%. The holder of the long position pays an amount of cash (in the form of an

upfront premium) corresponding to the volatility level of the contract. On expiry, if the spot yield of the

R153 is lower than the strike level, the holder of the option will be delivered R1 million R153 at a price

corresponding to the strike level.”

TABLE 5.10: SPECIFICATIONS OF LISTED BOND OPTIONS

Contract code

BO-Instrument-expiry-put\call

(e.g. BOR194 Dec04P)

Underlying instrument Various (e.g. R194, R157)

Contract size Notional amount agreed by counterparties

Contract months 1st Thursday of February, May, August and November

Expiry date and time 1st Thursday of February, May, August and November at 12h00

Quotations Implied volatility

Minimum price movement 4th decimal place (0.0001%)

Standard quote size R1 million

Expiry price valuation method As per BESA MTM process

Settlement Physically settled by reporting the bond transaction through the exchange or cash

settled

Margin requirements Agreed bi-laterally between the parties

59 www.bondexchange.co.za

163

5.10.5 Options on bond indices

A bond index option may be defined as an option to buy (call) or sell (put) a specific bond index on or before

an expiry date at a pre-specified price (not rate; rate applies to options on specific bonds). There are three

bond indices in South Africa (called the Total Return Indices (TRI); they were launched by BESA in 2000):

• All Bond Index (ALBI), consisting of the most liquid sovereign [i.e. RSA (central government)] and

non-sovereign (e.g., local government, public utilities and corporate) bonds.

• Government Bond Index (GOVI), containing those RSA bonds of the ALBI in which the primary dealers

make a market, i.e. the most liquid bonds.

• Other Bond Index (OTHI), being the non-RSA bonds in the ALBI basket.

The indices enable investors to measure the performance of bonds of various terms. Bond options are

written on some of these indices, but particularly on the GOVI. The market is also of the OTC variety

5.10.6 Bond warrants (call options)

There are two types of bond warrants:

• Bond warrants (retail options).

• Bond warrants (call options).

The term “bond warrant” internationally refers to call options on specific bonds but with a difference: when

a bond warrant (call option) is exercised, this leads to the issuer issuing new bonds. In the case of the

ordinary bond options, the issuer is not involved - the writer of a call that is exercised sells existing bonds to

the holder of the option.

The term to expiry of bond warrants (call options), unlike normal options, is long, sometimes running for

many tears. The underlying bond also has a long term to maturity, usually 10 years or longer.

This warrant-type does not exist in South Africa.

5.10.7 Bond warrants (retail options)

In South Africa, however, the term “bond warrant” refers to ordinary options on specific bonds, but they are

retail options, i.e. the denominations are small. Calls and puts are written and traded and a call does not lead

to the issue of new bonds. Certain banks are involved in this market and they are the market makers. These

warrants are listed.

A particular bank that is substantially involved in this market explains60:

“SB bond warrants give investors the opportunity to trade their view on the bond yield of the RSA R153

government bond and hence profit from movements in interest rates. SB bond call warrants are used to

profit from increases in the bond price (decreases in yields) and conversely SB bond put warrants are used to

profit from decreases in the bond price (increases in yield).

60 A past division of Standard Bank, SCMB. See www.warrants.co.za. Cosmetic language and other small changes have been made.

We have substituted Standard Bank (SB) for SCMB.

164

“Benefits of SB bond warrants”

• A convenient short-term trading or hedging facility.

• Easily traded - listed on the JSE.

• Cash settled at maturity.

• Calls and puts.

• Transact via any stockbroker including discount and on-line brokers.

• Market liquidity provided by SB.

• Maximum loss limited to initial investment.

• No margin calls.

“How do SB bond warrants work?”

• SB Bond warrants are similar to equity warrants, however, they are based on the R153 bond yield,

i.e. the yield of the government issued R153 bond, which is commonly traded.

• The warrants will be cash settled at maturity - there is no need or obligation for the investor to

receive or deliver the underlying bonds in any circumstance.

• SB bond warrants are based on an R153 bond with a nominal face value of R100.00. To express this

in comparable terms to equity warrants, the bond warrant will carry a conversion ratio of 10:1,

meaning that 10 warrants relates to one R100.00 nominal face value R153 Bond.

• Calls. SB bond call warrants will pay a settlement amount at maturity equal to the amount by which

the bond price exceeds the exercise price, if any. Accordingly, the value of SB bond call warrants

tends to increase if the price of bonds increases and therefore the bond yield falls.

• Call Terms 11.5% 10:1 7th November, 2002 European call, cash settled. 11.5% 10:1 6th February,

2003 European call, cash settled.

• Puts. SB bond put warrants will pay a settlement amount at maturity equal to the amount by which

the bond price is below the exercise price, if any. Accordingly, the value of SB bond put warrants

tends to increase if the value of bonds decreases and therefore the bond yield rises.

• Put terms. 12.25% 10:1 7th November, 2002 European put, cash settled. 12.5% 10:1 6th February,

2003 European put, cash settled.

“What happens at settlement?”

Example:

Warrant Code: 1R153SB

Type: European put

Strike: 11.50%

Expiry: 10th May 2002

Conversion ratio: 10:1 (underlying R100.00 nominal face value bond)

Spot yield at expiry: 12.03%

Number of warrants held by the investor: 10 000

Settlement: cash settled only

Strike price of the bond warrant (per 10 warrants): R110.52

165

Spot price of the bond at warrant expiry (per 10 warrants): R107.64

Settlement price (per 10 warrants): R2.88 (R110.52 - R107.64)

Therefore the investor will receive a cash settlement amount of R2880.00 (i.e.: R2.88 x 1000)

“What are the risks associated with SB bond warrants?”

SB bond warrants are primarily exposed to changes in the underlying bond yield and to changes in interest

rates. The warrants are also exposed to changes in the expected bond prices and time to expiry.

As with equity warrants, SB bond warrants are a leveraged investment. Like other leveraged investments,

they provide more exposure in percentage terms to both increases and decreases in the underlying bond

yield when compared with investing directly in bond directly.

For a further, more detailed examination of the risks and obligations associated with SB Bond warrants,

potential investors should read the offering document.”

“5.10.8 Callable and puttable bonds (bonds with embedded options)”

Bonds with embedded options are bonds that are issued with provisions that allow the issuer to repurchase

(callable bond) the bond, or the holder to sell back to the issuer (puttable bond) the bond at a pre-specified

price/rate at certain dates in the future.

The callable bond means that the buyer of the bond has sold to the issuer a call option to repurchase the

bond. The strike price/rate (also called the call price) is the pre-determined price/rate that the issuer is

obliged to pay to the bondholder.

It is usual that callable bonds are not callable for some years after issue. For example, a 15-year bond may

not be callable for 10 years, and a price is set for each year after 10 years. A portion of the bond or the full

amount may be callable. The fact that the buyer has “sold” to the issuer a call option means that these

bonds are issued at a lower price (higher rate) than equivalent term and rated “ordinary” bonds.

Puttable bonds, i.e. bonds with embedded put options, are also issued in some markets. As noted, such

bonds have provisions that allow the holder to sell the bond back to the issuer at pre-specified prices/rates

on pre-determined dates. This means that the holder of the bond has bought a put option from the issuer.

These bonds are issued and trade at lower yields (higher price) than equivalent term and rated bonds

without such options attached.

5.10.9 Convertible bonds

Convertible bonds are bonds that are convertible into shares (ordinary or preference) at the option of the

holder on pre-specified terms (e.g. number of shares per nominal value).

166

5.11 OPTIONS ON EQUITY MARKET INSTRUMENTS



5.11.1 Introduction

We repeat our illustration on options introduced earlier for the sake of orientation (see Figure 5.17).

OPTIONS

debt market

forexmarket


marketbond market

equity market





Options on equities may be divided into the following categories:

• Options on specific equities.

• Options on equity indices.

• Equity warrants (call options).

• Equity warrants (retail options).

• Redeemable preference shares.

Examples of the options in the first two categories are shown in Table 5.11 for the US market. The many

different exchanges involved in these markets will be noted. It is obvious that these markets are exchange-

traded, but it should be pointed out that there is also an OTC market in shares and these and other indices.

167

TABLE 5.11: EXAMPLES OF US MARKET OPTIONS ON EQUITIES

Type Exchange Share / index

Options on shares (stocks in US)

CBOE

AM

PB

PC

NY

Many specific shares (stocks)





Options on share (stock in US) indices

CBOE

CBOE

CBOE

AM

PB

PB

PB

Dow Jones Industrial Average

NASDAQ 100

S&P 100 index

Major market index

Gold

Oil service index

Utility index

CBE = Chicago Board of Trade. CME = Chicago Mercantile Exchange. LIFFE = London International Financial Futures Exchange. CBOE = Chicago Board

of Option Exchange. AM = American Exchange. PB = Philadelphia Exchange. PC = Pacific Stock Exchange. NY = New York Stock Exchange.

5.11.2 Options on specific equities

There are many exchanges in the US and the UK (and other markets including the JSE) that list and trade

options on specific equities. Such options are usually written on the shares that have a large market

capitalisation, and are well traded (i.e. liquid). An example is required (see Table 5.12).61

TABLE 5.12: LLOYDS TSB EQUITY OPTIONS (QUOTED ON LIFFE) (CURRENT PRICE 384 PENCE)

Strike price

Calls Puts

Dec Mar Jun Dec Mar Jun

360 27.0 33.0 38.5 0.5 7.5 12.5

390 6.5 14.5 22.0 10.0 22.0 27.0

In this example there are two strike prices, i.e. 360 pence and 390 pence at a time when the share in trading

at 384 pence. The limited number of strike rates and contract maturity dates ensure that there is liquidity in

the option contracts.

61 Example from Pilbeam, 1998.

168

There are two sets of prices quoted, i.e. one for call options and one for put options. For example, the June

call price at a strike price of 390 is 22.0 pence. This means that a buyer of this call option will pay 22 pence

per share. The minimum contract size is 100 shares; thus the option contract will cost the buyer GBP 220 (i.e.

the premium). The buyer of the call has the right but not the obligation to buy 100 Lloyds shares at a price of

390 pence and the cost of the option is GBP 220. Alternatively, a June put option at a strike price of 390 will

cost GBP 270 and this will bestow upon the buyer the right to sell 100 Lloyds shares at a price of 390 pence

at any stage up to the expiry date of the option in June.

The markets in options on individual shares are large, and they are usually exchange-traded. There are also

OTC markets in options on individual shares.

In 2006 the JSE (Equities Division)62 launched a new type of option on equities: the Can-Do Option. It is a

hybrid of an exchange listed option and an OTC option in that it is listed but has the flexibility of an OTC

option. It is therefore designed to, as stated by the JSE, “provide portfolio managers with a means to tailor

derivatives to their particular exposures.”

The following features distinguish it from other options on equities:

• Minimum contract size = R10 million (as such it is aimed at the professional investor).

• Contract size = any amount over R10 million.

• Underlying instruments = basket of shares can be specified by the investor.

• Expiry date = specified by the investor.

• Settlement = cash or physical at the option of the investor.

5.11.3 Options on equity indices

The options on indices markets of the world are also large and active. Examples of indices are the FTSE 100

in the UK, the DJIA and the S&P 500 in the US, the ALSI and the INDI in South Africa. They are mostly

exchange-traded, but an OTC market also exists.

An option on a share index allows the holder to take a position in the index (short or long) for the price of

the premium quoted. This means that to buyer of a share index is buying the right to “invest” in a diversified

portfolio (of the shares that make up the index) at a pre-specified price.

The value of index options is established by a multiplier that differs from index to index, i.e. the value of a

share index option is equal to the index times the multiplier. For example, the value of an option on the S&P

500 is IV x USD 500 (where IV = index value).

62 From Nomonde Mxhalisa., 2006. The new derivative in the investors armoury. The Financial Markets Journal, No 4.

Johannesburg: SAIFM.

169

In the case of the DJIAA it is IV x USD 100. If for example an option on the S&P 500 index is exercised at a

price of 1635, the amount involved is 1635 x USD 500 = USD 817 500. These options are settled in cash,

obviously because the index cannot be delivered.

An example may be constructive here:63 An investor has a portfolio that he set up to replicate the S&P 500

share index. He is concerned that monetary policy is about to be tightened and that share prices are about

to fall sharply, but he does not want to sell because it is expensive to sell and to reconstruct this portfolio

again after the fall (because of brokerage, taxes, etc). The value of his portfolio is USD 2.8 million and the

S&P 500 index is presently standing at 1395. The value of each option is thus 1395 x USD 500 = USD 697 500.

The investor will buy 4 put options on the S&P index. The strike price is 1400 and the term of the options is 3

months. Thus the investor is hedging his USD 2.8 million portfolio with 4 put options valued at USD 2 800

000 (4 x USD 500 x 1400).

If we assume that the investor is right in his view and the index falls from 1400 to 1120 (i.e. by 20% or 280

points). The value of the investor’s portfolio will be USD 2.24 million (remember he replicated the S&P 500

index with “physical” shares), i.e. a loss of USD 560 000. However, the investor exercises the 4 put options

on exercise date, and makes a profit of:

(1400 – 1120) x USD 500 x 4 = USD 560 000.

5.11.4 Equity warrants (call options)

As in the case of bond warrants, internationally equity warrants bestow the right (option) on the holder of

the warrant to take up new shares of the relevant company. These call options are long-term.

5.11.5 Equity warrants (retail options)64

The South African version of equity warrants (as in the case of bond warrants) is that they are ordinary

options (call and put options), but are small in size, i.e. retail. Exercising of a warrant does not lead to the

issue of new shares of the relevant company. Warrants are also written on equity indices.

Thus, South African warrants are short-term call / put options on specific shares and on certain indices. In

South Africa they are listed, and therefore are exchange traded. They are of the European option variety.

The first equity warrants in South Africa were issued in 1997. The issuers are equity market participants

(members of the JSE and merchant banks) that are independent of the companies whose shares underlie the

warrants.

After the JSE Committee grants approval, warrants are listed on the JSE and traded on the trading system.

They are traded in the same manner as any other security traded on the JSE.

If the Committee, or the President, suspends trading in a company, the listing of relevant warrants is

suspended. Warrants are settled through the JSE’s clearing system.

63 With some assistance from Saunders and Cornett, 2001. They also assisted with the currency option example.

64 See www.jse.co.za

170

As noted, warrants are written on specific shares and on certain indices. The most popular shares on which

warrants are written are Anglo, Gold Fields, Sasol, Harmony, Didata, Iscor, Bidvest, Remgro, and SABMiller.

The indices on which warrants are written are the All Share Index and the Industrial Index (ALSI and INDI).

5.11.6 Redeemable preference shares

Preference shares (“preferred stock” in other countries) in many countries are like perpetual bonds. In South

Africa, they are required to be redeemable or redeemable at the option of the issuer (section 98 of the

Companies Act, 61 of 1973).

5.12 OPTIONS ON FOREIGN EXCHANGE



We repeat our illustration on options introduced earlier for the sake of orientation (see Figure 5.18).

OPTIONS

debt market

forexmarket


marketbond market

equity market





Options on foreign exchange (also called currency options) are traded the world over, and the most tradable

contracts are those written on USD / EUR (example: EUR 62 500 on the PHLX), USD / JPY (example: JPY 12

500 000 on the PHLX), USD / GBP (example GBP 31 250 on the PHLX), USD / CAD (example: CAD 50 000 on

the PHLX), USD / AUD (example: AUD 50 000 on the PHLX). In the US, the Philadelphia Options Exchange

(PHLX) is particularly active in currency options.

The underlying asset in a currency option is an exchange rate. A call option on the GBP for example will give

the buyer the right to buy GBP for a given price in dollars (i.e. the strike price).

171

TABLE 5.13: PHILADELPHIA OPTIONS EXCHANGE GBP / USD OPTIONS

GBP 31 250 (CENTS PER POUND) (SPOT PRICE: GBP / USD 1.6383)

Strike price

Calls Puts

June July August June July August

1.63 1.5 2.4 2.9 1.1 1.55 2.23

1.64 1.3 1.84 2.35 1.5 2.01 2.62

1.65 0.94 1.43 1.89 1.05 2.55 3.21

An example is always useful (see Table 5.13). The GBP / USD spot price is GBP / USD 1.6383. The face value

of currency option contracts is fixed at an amount of currency; in this example it is GBP 31 250). A US

investor purchases a June GBP call option at an exercise / strike price of 1.63 (this of course means GBP /

USD 1.63). The face value of the contract is GBP 31 250.

At the end of the life of the option the GBP increases in value relative to the USD. We assume GBP / USD

1.76. The investor exercises the option and receives GBP 31 250 for which he pays USD 50 937.50 (1.63 x

GBP 31 250). The investor sells the GBP in the spot forex market at the spot exchange rate of GBP / USD

1.76, and receives USD 55 000 (1.76 x GBP 31 250). The profit made is USD 4 062.50 (USD 55 000 - USD 50

937.50) less the premium paid for the option.

The premium is quoted in US cents per GBP. In the above example the premium is 1.5 US cents per GBP, i.e.

the premium amount is 31 250 x 1.5 / 100 = USD 468.75. Total net profit is USD 3 593.75 (USD 4 062.50 –

USD 468.75).

5.13 OPTIONS ON COMMODITIES



The commodities options markets are also large markets internationally, but they fade into the background

when compared with the options on financial instruments markets. Options are written on all the larger

commodities, such as gold, oil, wheat, maize, soybean, and certain commodity indices such as the AMEX oil

index. The commodity options markets are both formalised and OTC.

172

5.14 OPTION STRATEGIES



5.14.1 Introduction

There are no fundamental dissimilarities between operations in the futures and options markets, i.e.

dealings in the options market can be divided into the four types:

• Speculative.

• Hedging.

• Arbitrage.

• Investment.

In addition, a virtually unlimited variety of payoff patterns may be attained by the combination of calls and

puts with various exercise prices. Here we consider only two of the combinations of options, the straddle

and the strangle.65

5.14.2 Straddle

TABLE 5.14: PROFIT / LOSS PROFILE OF A LONG STRADDLE

Underlying price of

share at expiry

Profit / loss on call

option

Profit / loss on put

option Net profit / loss on straddle

440

445

450

455

460

465

470

475

480

485

490

495

500

505

510

515

520

-10

-10

-10

-10

-10

-10

-10

-10

-10

-5

0

+5

+10

+15

+20

+25

+30

+31

+26

+21

+16

+11

+6

+1

-4

-9

-9

-9

-9

-9

-9

-9

-9

-9

+21

+16

+11

+6

+1

-4

-9

-14

-19

-14

-9

-4

+1

+6

+11

+16

+21


173

The straddle is generally put into place when an investor believes that the price of the underlying is about to

“run” but she is uncertain of the direction. The straddle involves the purchasing of a call and a put at the

same strike price and expiration date.

The share price of Company ABC is trading at 480 pence currently. The price of a call at a strike of 480 pence

is 10 pence and the price of a put at the same strike is 9 pence. The position is held to maturity (six months

from purchase). Table 5.14 and Figure 5.19 set out the profit and loss profile.

TABLE 5.15: VALUE OF STRADDLE AT EXPIRY

SPt < X SPt ≥ X

Payoff of call 0 SPt - X

+ Payoff of put X - SPt 0

= Total X - SPt SPt - X

Figure 5.19: profit / loss profile of a long straddle

payoff of straddle

payoff of put

SPt spot price at expiry



payoff of call

X = 480

-10 p

payoff

profit

payoff

payoff

profit

profit

-9 p

19 p

174

The solid line in the lowest part of the chart shows the payoff condition of the straddle. At X = SPt the payoff

is equal to zero. It is only at this point that the payoff is zero; at all other points the straddle has a positive

payoff. One may then ask why these combinations are not more popular. The answer is that if prices are not

volatile the holder may lose heavily because she is paying a much higher premium than is usually the case.

The dotted line in the chart represents the profit of the straddle. It is below the solid line by the cost of the

straddle, i.e. the premium, in this case 19 pence. This is the maximum that can be lost.

5.14.3 Strangle

A strangle is the same as the straddle except that the exercise prices differ. An example is shown in Table

5.16.66

The share price of Company ABC is trading at 480 pence. The price of a call option at strike 460 is 25 pence,

and the price of the put at strike 480 is 9 pence. The table shows the payoff profile. It will be clear that there

is a range where maximum losses are made and this is between the two strike prices. The loss is capped at

14 pence. Beyond this range the losses are reduced or profits rise and they do so in a symmetrical fashion.

TABLE 5.16: PROFIT / LOSS PROFILE OF A LONG STRANGLE

Underlying price of

share at expiry

Profit / loss on call

option

Profit / loss on put

option Net profit / loss on straddle

440

445

450

455

460 (call strike)

465

470

475

480 (put strike)

485

490

495

500

505

510

515

520

-25

-25

-25

-25

-25 (call premium)

-20

-15

-10

-5

0

+5

+10

+15

+20

+25

+30

+35

+31

+26

+21

+16

+11

+6

+1

-4

-9 (put premium)

-9

-9

-9

-9

-9

-9

-9

-9

+6

+1

-4

-9

-14

-14

-14

-14

-14

-9

-4

+1

+6

+11

+16

+21

+26


175

5.15 EXOTIC OPTIONS67



Securities broker-dealers and investment banks have over the years developed many so-called exotic

options. Many of them cross the various markets. The following may be mentioned as examples:

As you like it options (AYLIO)

The AYLIO is an option that allows the holder to convert from one type of option to another at a certain pre-

specified point prior to expiration. This is usually from a call to a put or vice versa. This option type is also

called “call or put option” or “chooser option”.

Average rate options (ARO)

The ARO is an option on which settlement is based on the difference between strike price and the average of

the share or index on certain given dates. The “average” attribute of the ARO renders this option less volatile

and thus cheaper than a conventional “spot price option”. The ARO is also called an “Asian Option”.

Barrier options (BAO)

There are many types of barrier options. Their payoff is dependent on the price of the underlying asset and

on whether the asset reaches a pre-determined barrier at any time in the life of the option. There are, for

example, knock-in options and knock-out options. The former is activated when the price of the underlying

asset reaches a pre-determined level. The latter option is “killed” if the price of the underlying reaches a pre-

determined level.

Compound options (CO)

A CO is an option on an option. The buyer has the right to buy a specific option at a preset date at a preset

price.

Lookback options (LO)

A LO is an option where the payout is determined by using the highest intrinsic value of the underlying

security or index over its life. For a lookback call the highest price is used, whereas the lowest price is used in

a lookback put.

Quantro options (QO)

A QO is a currency option in terms of which the foreign exchange risks in an underlying security have been

eliminated.

Package options (PO)

A PO is a portfolio consisting of standard European calls, standard European puts, forward contracts, cash

and the underlying asset itself. An example is a range forward contract.

67 See Pilbeam, 1998 and Hull, 2000.

176

Forward start options (FSO)

FSOs are options that start their life at some stage in the future. They are used in employee incentive

schemes.

Binary options (BIO)

BIOs are options with discontinuous payoffs. An example is a cash-or-nothing call. This pays off nothing if the

share price ends up below the strike price at some time in the future and pays a fixed amount if it ends up

above the strike price.

Shout options (SO)

SOs are European options where the holder can “shout” to the writer at one time during its life. At the end

of the life of the option the holder receives either the usual payoff from a European option or the intrinsic

value at the time of the shout whichever is greater.

Other options

There are also other options such as options to exchange one asset for another (exchange options), options

involving several assets (rainbow options), basket options, etc.


Outcomes

• Define an option.

• Understand the characteristics of an option.

• Know the different types of, and concepts relating to options.

• Understand the payoff profiles of the various option types.

• Comprehend intrinsic value and time value.

• Understand the motivation for undertaking (buying or writing) option contracts.

Review questions

1. Writers exercise their options only if it is rewarding to do so, and their potential loss is finite, while their

potential profit is limited to the premium received for the option. True or false?

2. Call and put options both give the holder the right to decide whether to exercise the option. In the

former case the writer is obliged to sell the underlying asset if the option is exercised, whilst in the latter

case the writer is obliged to buy the underlying asset if the option is exercised. True or false?

3. The buyer of a call option takes a long option position and the buyer of a put option takes short option

position. True or false?

4. The strike (or exercise) price on a put option is R500 and the premium paid was R10. On the expiration

date the spot price is R495. The holder will not exercise the option because the spot price plus the

premium is more than the strike price. True or false?

5. An option that is at-the-money (ATM) has no intrinsic value because SP = EP but does have time value

because it has not yet reached its expiry date. True or false?

177

6. Call options are more valuable as the SP of the underlying asset increases, and less valuable as the EP

increases. Put options are more valuable as the SP of the underlying asset decreases and less valuable as

the EP increases. True or false?

7. The longer the time to expiration the more valuable both call and put options are because the accrued

interest calculated at the risk-free rate will be more the longer the period until maturity. True or false?

8. The Black-Scholes option pricing model is referred to as the Midas formula, because it allows the investor

to avoid all risk and obtain a true risk-free investment. True or false?

9. Define an option.

10. What are the types of underlying assets in the financial markets on which options can be acquired?

11. What will be the profit or loss payoff of the writer of a call option if the spot price should fall below the

strike (or exercise) price and if the spot price should rise above the strike price?

12. What will be the profit or loss payoff of the holder of a put option if the spot price should fall below the

strike (or exercise) price and if the spot price should rise above the strike price?

13. For each of the following options, state whether it is a horizontal flip image (left flips to right and vice

versa), or vertical flip image (top goes to bottom, etc), or both a horizontal and vertical flip image of the

payoff profile of call option from the perspective of the holder of a call option; writer of a call option;

holder of a put option; and writer of a put option.

14. You are given the following information about a put option:

Underlying asset = a share listed on the JSE

Underlying asset spot market price (SP) = R243

Option exercise price (EP) = R251

Premium (P) = R12.

What is the time value on this option?

15. What variable in the Black-Scholes model is the key determinant of the probability distribution of the

underlying asset price? Why is this variable in the equation for the calculation of the value of a European

option?

16. Why do the values of both puts and calls increase as volatility (of the underlying asset price) increases?

17. An investor requiring a general equity exposure to the extent of R1 million decides to acquire this

exposure through the purchase of call options on the ALSI future. The index is currently recorded at 12

500. Assume that the premium is R1 700 per contract. How many option contracts would the investor

require? What is the investor's breakeven price?

18. The premium on a 3-month JIBAR September future, with a price of R94.60%, is 8.5% in June. An investor

buys a call option on this future in June for a nominal value of R1 000 000. By the expiry date interest

rates have fallen to 5.2%. Will the holder exercise the option and what is the profit or loss on the option?

178

19. An investor has a portfolio that can be compared with the JSE's ALSI share index. The value of his

portfolio is R5.5475 million and the ALSI index is presently standing at 15 850. The value of a share index

option is ten times the index value. How many put options will the investor require to hedge the value of

his portfolio?

Answers

1. False. Writers do not exercise their options; holders have the right, granted to them by the writers, to

exercise their options, which they will only do if it is rewarding to do so. The potential loss to the writer is

not finite, while their potential profit is limited to the premium paid for the option.

2. True.

3. False. The buyer of an option (call or put) takes a long position, i.e. s/he has bought the option and has

the benefits of the option (the “option” to do something). The seller of an option (call or put) has taken a

short position, i.e. s/he has sold the option and received the premium.

4. False. The holder will exercise the option because doing so will reduce the net loss from R10 (the

premium) to R5. The option is bought at the spot price of R495 and sold at the strike price of R500. That

gives a profit of R5 that reduces the cost of the premium of R10 by R5, leaving a net loss of R5.

5. True.

6. True.

7. False. The longer the time to expiration the more valuable both call and put options are because the

holder of a short-term option has certain exercise opportunities, whereas the holder of a similar long-

term option also has these opportunities and more. Therefore the long option must be at least equal in

value to a short-term option with similar characteristics. As noted above, the longer the time to

expiration the higher the probability that the price of the underlying assets will increase/decrease

because it is probable that the fluctuation of the price can produce a spot rate that will make a bigger

profit possible in future (but before expiration) than can be made today.

8. The Black-Scholes option pricing model is not the Midas formula, because it rests on a number of

simplifying assumptions such as the underlying asset pays no interest or dividends during its life, the risk-

free rate is fixed for the life of the option, the financial markets are efficient and transactions costs are

zero, etc. However, it is very useful in the case of certain options.

9. An option bestows upon the holder the right, but not the obligation, to buy or sell the asset underlying

the option at a predetermined price during or at the end of a specified period.

10. The underlying assets in the options markets of the world are other derivatives (futures and swaps), and

specific instruments (“physicals”) and notional instruments (indices) of the various markets.

11. If the spot price falls below the strike price: the writer will make a profit equal to the premium. If the spot

price rises above the strike price: the writer will make a loss that is unlimited in the sense that it will rise

in proportion to the rise of the spot price above the strike price.

179

12. If the spot price falls below the strike price: the holder will make a profit that is unlimited in the sense

that it will rise in proportion to the fall of the spot price below the strike price. If the spot price rises

above the strike price: the holder will make a loss that is equal the premium paid on the option.

13. Payoff profile of the writer of a call option: a vertical flip image of the payoff profile of the holder of a call

option.

Payoff profile of the holder of a put option: a horizontal flip image of the payoff profile of the holder of a

call option.

Payoff profile of the writer of a put option: a horizontal and vertical flip image of the payoff profile of the

holder of a call option.

14. R4 {12 – (251 – 243)}.

15. The volatility of the underlying asset is the key variable in the Black-Scholes model that determines the

probability distribution of the underlying asset price. This is in the calculation of the value of the option

as the intrinsic value of the option is the difference between the strike (or exercise) price and the

(future) spot price. The former is known and fixed whereas the latter is unknown and uncertain. If the

past fluctuations in the price of the underlying asset (its volatility) will be repeated in the future, it

provides a statistical basis (the probability distribution) for forming an expectation of the future spot

price.

16. As volatility increases, so does the chance that the underlying asset will do well or badly. The direct

investor in such an asset will not be affected because these two outcomes offset one another over time.

However, in the case of an option holder the situation is different:

• The call option holder benefits as prices increase and has limited downsize risk if prices fall;

• The put option holder benefits as prices decrease and has limited downsize risk if prices rise.

Thus, both puts and calls increase in value as volatility increases.

17. An investor requiring a general equity exposure to the extent of R1 million decides to acquire this

exposure through the purchase of call options on the ALSI future. The index is currently recorded at 12

500, s/he would require 8 call option contracts (8 x R10 x 12500 = R1 000 000) (remember that one

ALSI futures contract is equal to R10 times the index value).

Because the investor is buying the right to purchase the future and has no obligation in this regard,

s/he pays a premium to the writer. The premium is R1 700 per contract (R13 600 for 8 contracts). The

investor is thus paying R13 600 for the right to purchase 8 ALSI futures contracts at an exercise or strike

price of 12500 on or before the expiry date of the options contract. It will be evident that the

premium per contract of R1 700 translates into 170 points in the all share index (R1 700 / R10

per point). Thus, the investor’s breakeven price is 12670 (12500 + 170).

18. The holder of the option has the right to make a deposit of R1 000 000 on the expiry date in September

(the date is specified) at an interest rate of 5.4% (100 – 94.60) for 3 months.

Each tick movement on the contract, which is equivalent to one basis point, is worth the value of the

contract (R1 000 000) multiplied by 1 basis point (0.01% or 0.0001) and a quarter of a year (0.25),

i.e.: R1 000 000 x 0.0001 x 0.25 = R 25.00.

180

The cost of the call option (i.e. the premium), is therefore 8.5 x R25.00 = R212.50.

If by the expiry date the contract strike price rises to R94.80% (interest rates have fallen to 5.2%)

the holder is entitled to a gain of 20 basis points, and the profit is 20 x R25.00 = R500.00 less the

premium of R212.50 = R287.50.

The holder will therefore exercise the option to make a profit of R287.50.

19. The value of his portfolio is R5.5475 million and the ALSI index is presently standing at 15 850. The value

of a share index option is ten times the index value. The value of each option is thus 15 850 x R10 = R158

500. The investor will buy 35 put options on the ALSI index (35 x 158 500 = 5 547 500).


Options listed on Yield-X:


Options listed on BESA:

http://www.bondexchange.co.za/besa/action/media/downloadFile?media_fileid=2887

Options tutorial:

http://www.888options.com/about/default.jsp

Examples of SA exotic options:

http://corporateandinvestment.standardbank.co.za/trading/equity/productsandservices.html

181

CHAPTER 6: OTHER DERIVATIVE INSTRUMENTS


THIS CHAPTER (6) WILL NOT BE EXAMINED




Chapter 2 Forwards

Chapter 3 Futures

Chapter 4 Swaps

Chapter 5 Options



After studying this chapter the learner should:

• Comprehend the existence of derivatives that are not classified under the traditional derivatives

(forwards, futures, swaps and options).

• Understand the derivative product: products of securitisation.

• Understand the derivative product: credit derivatives.

• Understand the derivative product: weather derivatives.

6.3 INTRODUCTION

The mainstream derivatives were discussed above. As stated before, derivatives are instruments that cannot

exist without their underlying instruments and their value depends on the value of these underling

instruments; and the traditional underling instruments are share prices, share indices, interest rates,

commodity prices, exchange rates, etc.

Over the past decades, and in some cases over the past few years, other derivatives have been developed

that are based on the prices of other underlying variables. For example, the following derivatives are

available in international markets):

• Securitisation.

• Credit derivatives.

• Weather derivatives.

• Insurance derivatives.

• Electricity derivatives.

182

Insurance derivatives have payoffs that are dependent of the amount of insurance claims of a specified type

made during the period of the contract. Electricity derivatives have payoffs that are dependent on the spot

price of electricity. Here we briefly discuss the other three mentioned.

6.4 SECURITISATION

The products of securitisation may also be seen as “derivatives” because they and their prices are derived

from debt or other securities that are placed in a legal vehicle such as a company or a trust. Some analysts

will insist that these products are not derivatives. However, the jury is still out in this respect.

Securitisation amounts to the pooling of certain non-marketable assets that have a regular cash flow in a

legal vehicle created for this purpose (called a special purpose vehicle or SPV) and the issuing by the SPV of

marketable securities to finance the pool of assets. The regular cash flow generated by the assets in the SPV

is used to service the interest payable on the securities issued by the SPV.

There are many assets (representing debt) that may be securitised, and the list includes the following:

• Residential mortgages.

• Commercial mortgages.

• Debtors’ books.

• Credit card receivables.

• Motor vehicle leases.

• Certain securities with a high yield.

• Equipment leases.

• Department store card debit balances (examples: Edgars card and Stuttafords card).

For the banks, securitisation amounts to the taking of assets off balance sheet and freeing up capital68. For

companies, securitisation presents an alternative to the traditional forms of finance. An example of the

latter is the securitisation of company’s debtors’ book.

A typical securitisation (of mortgages) may be illustrated as in Figure 6.1. In this example, the bank decides

to securitise part of its mortgage book, in order to free up the capital allocated to this asset. It places R5

billion of mortgages into a SPV, and the SPV issues R5 billion of mortgage-backed securities (MBS) at a

floating rate benchmarked to the 3-month JIBAR to finance these assets. A portfolio manager manages the

SPV, and trustees appointed in terms of the scheme monitor the process on behalf of the investors (in this

case assumed to be pension funds) in the MBS.

68 Not always though; it depends on credit enhancement facilties.

183

Figure 6.1: simplified example of bank securitisation of mortgages

equity and liabilitiesassets

BANK (ZAR MILLIONS)

mortgages -5 000 deposits -5 000


SPV (ZAR MILLIONS)

mortgages +5 000 MBS +5 000


PENSION FUND (ZAR MILLIONS)

MBS +5 000 deposits - 5 000

originator = bank

portfolio manager =

servicer

trustees = watchdog

bankruptcy-remote

MBS credit-

enhanced


BANK (ZAR MILLIONS)

mortgages -5 000 deposits -5 000


SPV (ZAR MILLIONS)

mortgages +5 000 MBS +5 000


PENSION FUND (ZAR MILLIONS)

MBS +5 000 deposits - 5 000

originator = bank

portfolio manager =

servicer

trustees = watchdog

bankruptcy-remote

MBS credit-

enhanced

It should be noted that the details of the above securitisation have been ignored, in the interests of

understanding the basic principles of the transaction. In real life, the scheme is extremely lawyer-friendly,

and the MBS issued are rated AAA by the rating agency/agencies in order to attract investors. This is

achieved by the credit-enhancement process, by which is meant that the SPV is properly “capitalised”. The

latter in turn is achieved by the SPV issuing 3 streams of MBS in the following manner (this is an example)69:

• AAA rated MBS: 90% of the total (i.e. R4 500 billion).

• BBB rated MBS (called mezzanine debt): 7% of the total (i.e. R350 million).

• Unrated MBS (called subordinated debt): 3% of the total (i.e. R150 million).

The AAA rated paper, as noted, is sold to the market, while the BBB paper is usually purchased by one of the

sponsors at an excellent rate of interest.70 The management company usually holds the unrated paper in

portfolio, and a mixture of equity and debt finances this company.

The variable rate of interest paid on the underlying assets (and the cost of the credit enhancement)

determines the rate payable on the three streams of paper created by the SPV.

69 There are other requirements as well, such as a liquidity requirement.

70 As high as 400 basis points above the AAA-rated paper (ie + 4%).

184

6.5 CREDIT DERIVATIVES

6.5.1 Introduction

Credit derivatives emerged in the 1990s, and the market and the range of products have grown significantly

since then. A credit derivative may be defined as “… a contract where the payoffs depend partly upon the

creditworthiness of one or more commercial or sovereign entities.”71 There are a number of credit derivative

contracts, such as total return swaps (e.g. where the return from one asset is swapped for the return on

another asset), credit spread options (e.g. an option on the spread between the yields on two assets; the

payoff depends on a change in the spread) and credit default swaps. The latter is the most utilised credit

derivative72, and we focus on this one below.

6.5.2 Example of credit default swap

A credit default swap is a bilateral contract between a protection purchaser and a protection seller that

compensates the purchaser upon the occurrence of a credit event during the life of the contract. For this

protection the protection purchaser makes periodic payments to the protection seller. The credit event is

objective and observable, and examples are: default, bankruptcy, ratings downgrade, and fall in market

price.

protection buyer(PB)

protection seller(PS)

fee(default swap

spread)

par valueof bond of

reference entity (upon default)

physical bondof reference

entity(upon default)

protection buyer(PB)

protection seller(PS)

fee(default swap

spread)

par valueof bond of

reference entity (upon default)

physical bondof reference

entity(upon default)

Figure 6.2: example of a credit default swap

An example is required (default by an issuer of a bond): a credit default swap contract in terms of which

INVESTCO Limited (an investor; called the protection buyer) has the right to sell a bond73 issued by DEFCO

Limited (a bond issuer; called the reference entity) to INSURECO Limited (an insurer; called the protection

seller) in the event of DEFCO defaulting on its bond issue (the specified credit event). In this event the bond

is sold at face value (100%).

71 Definition from Hull (2000: 644)

72 Estimated by the British Bankers’ Association at close to 40% of the market (in 1999).

73 Some contracts are also settled in cash.

185

In exchange for the protection, the protection buyer undertakes to settle an amount of money (or fee) in the

form of regular payments to the protection seller until the maturity date of the contract or until default. The

fee is called the default swap spread. This contract may be illustrated as in Figure 6.2.74

As noted, the fee is payable until maturity of the bond or until default. If default takes place, the protection

buyer has the right to sell the bond to the protection seller at par value. It is then up to the protection seller

to attempt to recover any funds from the defaulting bond issuer. The following are the details of the

contract:75

Protection buyer = INVESTCO Limited

Protection seller = INSURECO Limited

Reference entity (issuer) = DEFCO Limited

Currency of bond = ZAR

Maturity of bond = 3 years

Face value = ZAR 30 million

Default swap spread = 35 basis points pa

Frequency = Six monthly

Payoff upon default = Physical delivery of bond for par value

Credit event = Default by DEFCO Limited on bond.

12 m0 m 18m 24 m 30 m6 m

ZAR52 500

ZAR52 500

ZAR52 500

ZAR52 500

ZAR52 500

ZAR52 500

36m

at maturity protection buyer cashes in bond for par value

Figure 6.3: cash flows with no default (to protection seller)

The cash flows in the event of no default and default are as shown in Figure 6.3 and Figure 6.4.

74 Example much adapted from Lehman Brothers International (Europe), 2001.

75 Ibid.

186

ZAR52 500

credit event(default)

12 m0 m 18m 24 m 30 m6 m 36 m

ZAR52 500

ZAR52 500

protection buyer delivers bond to protection seller in exchange for par value = ZAR 30 million

Figure 6.4: cash flows in event of default

6.5.3 Pricing

The pricing of credit derivatives is straightforward. The fee payable on the swap, i.e. the default swap spread

(DSP), should be equal to the risk premium (RP) that exists over the risk-free rate (rfr = rate on equivalent

term government bonds). In other words, the DSP should be equal to the RP which is equal to the yield to

maturity (ytm) on the DEFCO bond less the rfr:

DSP = RP = ytm – rfr.

This is so if the credit default swap is priced correctly. If this is not the case, arbitrage opportunities arise. For

example, if rfr = 10.0% pa and RP = 5.0% pa then ytm = 15.0% pa. If the market rate (ytm) of the reference

bond is 17.0% pa, and DSP = 5.0% pa, it will pay an investor (protection buyer) to buy the bond at 17.0% pa

and do the credit swap (cost = 5% pa) because he is getting a 200bp better return than the rfr (10% pa) on a

synthetic risk-free security.

Conversely, if the ytm of the reference bond is 13.0% pa, and DSP = 5.0% pa, it pays the protection seller to

short the reference bond and enter into the swap. This means that the protection seller is borrowing money

at 13% pa (the ytm at which the reference bond is sold), and investing at the rfr (10.0% pa) and earning the

DSP of 5.0% pa, i.e. a profit of 200 bp.

Clearly these examples point to the fact that arbitrage will ensure that in an approximate sense DSP = RP.

The main participants in the credit derivatives market are the banks (63% of protection buyers and 47% of

protection sellers), securities firms (18% of protection buyers and 16% of protection sellers) and insurers (7%

of protection buyers and 23% of protection sellers).76 The other participants are the hedge funds, mutual

funds, pension funds, companies, government, and export credit agencies.

76 Estimates by the British Bankers’ Association in 1999.

187

6.6 WEATHER DERIVATIVES

6.6.1 General

The weather derivative is a relatively new instrument, but it is growing in popularity because many

businesses depend on or are affected by the weather. Examples are:

• Retailers in London (example: loss of sales in bad weather).

• Agricultural concerns (example: loss of crops).

• Insurers of agricultural concerns (example: claims for hail damage)

• Construction enterprises (example: loss of time spent on a contract as a result of inclement

weather).

• Football stadiums (example: lower turnstile takings as a result of bad weather).

• Large landlords (example: additional heating costs in cold periods).

According to Applied Derivatives Trading Magazine77, 75% of the profits of enterprises rise and fall as a result

of the vagaries of the weather. The magazine also reported that in the first 18 months since weather

derivatives were introduced some 1 000 contracts were signed.

Weather derivative contracts are executed in a fashion as instruments such as caps, floors, collars, swaps,

etc, and are settled in the same way as these. The counterparties to the hedgers use data supplied by

independent organisations such as the weather service data stations located at major airports.

The underlying “instrument” or “value” in the case of temperature-related weather derivatives is Celsius-

scale temperature as measured by “degree days” (DD). A DD is the absolute value of the difference between

the average daily temperature and 18oC. The winter measure of average daily temperature below 18oC is

called heating degree days (HDDs), and the summer measure of average daily temperature above 18oC is

termed cooling degree days (CDDs).

If for example the mean temperature of a day in December were 3oC, the HDD would be 15. The number for

the month is the total of the daily HDDs (negatives are ignored).

Weather hedges can be based on temperature, rainfall, etc, but the most common is contracts based on

DDs. Examples of contracts:

• Caps (also known as call options) establish a DD ceiling. The holder is compensated for every DD

above the ceiling up to a maximum amount.

• Floors (also known as put options) establish a DD minimum. The holder is compensated for every DD

below the floor up to a maximum amount.

• Collars or swaps establish a DD ceiling and a DD floor. The holder is compensated for every DD above

the ceiling or below the floor.

77 See Applied Derivatives Trading Magazine (November 1998).

188

An example follows78. A London retailer reviews historical weather and revenue data to uncover the

correlation between temperature and sales. They find that 225 HDDs in December is the point below which

winter apparel sales start to fall. Each DD below 225 corresponds to a potential GBP 10 000 in lost sales. The

retailer decides to buy a weather floor for December of 225 HDDs, with a payout of GBP 10 000 per DD and a

maximum of GBP 1 million. The weather index used is the weather station at London Weather Centre. The

premium is GBP 85 000.

December passes and the data is available on 3 January. The December cumulative number of HDDs is 200

(i.e. 25 below the floor of 225), i.e. it was warmer and winter apparel sales were indeed down. The seller of

the hedge pays out:

GBP 10 000 x 25 = GBP 250 000,

and the total income of the retailer is:

GBP 250 000 – GBP 85 000 (the premium paid) = GBP 165 000.

6.6.2 South African weather derivatives

The first South African weather derivative saw the light in October 200279. In its launch document Gensec

Bank provided some general details on these instruments:

“Who is Gensec Bank?”

A leading South African investment bank, specialising as a wholesale provider of derivative-based risk

management products to the savings industry. It is also a prominent arranger of debt and equity finance for

corporates and is a manager of private equity funds. Through its proprietary trading desk the bank acts as a

market maker in most South African financial instruments

“What is a weather derivative?”

A weather derivative is a financial instrument whose value depends on the value of some underlying

variable(s), in this case a weather index such as heating degree-days, cooling degree-days, average

temperature or millimeters of precipitation.

“What is the objective of weather derivatives?”

The underlying of weather derivatives is based on data, such as temperature, which influence the trading

volume of other goods. This in turn, means that the objective of weather derivatives cannot be to hedge the

price of the underlying, as it is impossible to put a rand value (price) on the various facets of weather. The

primary objective of weather derivatives is thus to hedge volume risks, rather than price risks, that result

from a change in the demand for goods due to a change in weather.

78 Clemmons, L and Mooney, N (1999)

79 Issued by Gensec Bank Limited. Minor cosmetic changes have been made to the text provided and the example.

189

“Why would one use weather derivatives rather than insurance?”

Weather derivative products offer weather-sensitive industries a risk management tool that allows them to

efficiently hedge weather risks that were previously uninsurable. Weather derivatives are struck close to the

mean to cover non-catastrophic events and unlike insurance they are contracts of difference, not a contract

of indemnity. ISDA (International Settlements Derivatives Association) documentation and a specific

confirmation process govern settlement.

“Do I have to prove that I have suffered loss before a weather derivative will pay out?”

No. Weather derivatives are not insurance contracts and are not linked to your actual loss. You may or may

not suffer loss as a result of a certain weather event occurring. Any payout you receive pursuant to a

weather derivative will be unrelated to whether you have actually suffered loss or the extent of any loss.

“Why has the weather derivative market developed?”

The deregulation of the energy sector created significant demand for weather risk management programs in

the US energy sector. Subsequently there has been an increased understanding and demand from weather

sensitive corporations.

“Who are the market participants?”

In the US there are over 70 market players. The market can be divided into two classes. The ‘primary’ or ‘end

user’ market are those institutions that face weather risk in their original business, such as construction

companies, agricultural businesses and amusement parks. The ‘secondary’ market is predominately the field

of investment banks, and trading houses specialising in weather derivatives, the objective being structuring,

trading and arbitrage profits. It is not the aim of most secondary market players to assume risk.

“What proportion of deals transacted has been for the primary market?”

The majority of deals transacted to date involve trading between institutional or professional dealers

(secondary market), rather than end-users (primary market), although there is a growing trend towards

deals with end-users.

“How many weather locations are there in South Africa?”

Over 500 weather stations. The weather data from these locations will gradually become available on the

Gensec Bank website.

“What sizes can Gensec Bank quote for a weather derivative transaction?”

Gensec Bank will normally make prices on structures with minimum payout of R100 000 and a maximum

payout of R5 million.

190

“What is the maximum term for a weather derivative structure?”

Gensec Bank will look at transactions as long as three years (multi-year deals). It is expected though that

most transactions will be seasonal. The longer the selected period, the more a weather option resembles an

Asian option (average rate options). Most contracts refer to a single season comprising several months, such

as the winter season from June to August.

“How is a weather derivative trading book managed?”

Weather trading books are actively managed by diversification globally, incorporating short-term forecasts,

evaluating the hedge potential of transactions and actively managing positions.

“How are weather derivatives priced?”

The burning cost method (historical burn) is the simplest method. The historical payout of the transaction

per year is determined for a specific period (strike +/- weather index multiplied by the tick size). The mean

plus a multiple of the historically determined standard deviation of the payouts used to calculate the so-

called burning cost premium. The burning cost method does not give adequate consideration to either

weather trends or to current meteorological developments (El Nino, global warming). Pricing therefore

consists of a mixture of burning cost and standard option price models in combination with actuarial

weather forecast information.

“When is the premium on a cap or floor structure payable?”

Premium payment is due two business days after the trade date.

“When is settlement made after the calculation period?”

The settlement date is the fifth business day after the calculation period.

“What happens if the weather index station for a transaction fails?”

All weather transaction confirmations outline two fallback stations and a fallback methodology in the

situation where the Index Station’s data cannot be used.”

The specifications of the first weather derivative contract were provided to the author in the following form

(title: “critical frost day”):80

“A deciduous farmer in the Western Cape faces the potential risk of frost damage during the spring season,

coinciding with the plants budding phase. Analysis indicates that a minimum temperature of below or equal

to 0 degrees Celsius has the potential to damage the crop. We provide a product that will compensate the

farmer for each such ‘frost day’.”

80 With thanks to Gensec Bank Limited. Minor cosmetic changes have been effected.

191

TABLE 6.1: SPECIFICATIONS OF THE FIRST WEATHER DERIVATIVE CONTRACT

Index Minimum daily temperature

Station Ceres Excelsior, South Africa

Critical event ‘Frost Day’ i.e. any day within the calculation period on which the hourly

temperature is less than or equal to 0 degrees Celsius

Period October 1, 2002 - November 30, 2002

Client position Buyer

Strike 0 days

Tick size R1 000 000 per day

Max payment R3 000 000 (3 days)

Premium R 300 000

6.7 SUMMARY OF DERIVATIVE INSTRUMENTS

We present a summary of the derivatives covered thus far (excluding the exotic options) in Table 6.2.

TABLE 6.2: SPOT MARKETS AND DERIVATIVE INSTRUMENTS

SPOT MARKETS

Derivatives Debt market Equity

market

Forex

market Commodity markets

Forwards

Forward interest rate contracts Yes

Repurchase agreements Yes

Forward rate agreements Yes

Outright forwards Yes Yes Yes Yes

Foreign exchange swaps Yes

Forward forwards Yes

Time options (obliged to exercise) Yes

Forwards on commodities Yes

Forwards on swaps1

Yes

Futures

On specific instruments (“physicals”) Yes Yes Yes Yes

On notional instruments (indices) Yes Yes Yes Yes

Swaps

Yes2

Yes3

Yes4

Yes5

Options

Options on futures Yes Yes Yes Yes

Options on swaps Yes

Options on specific instruments Yes Yes Yes Yes

Options on notional instruments Yes Yes Yes Yes

Interest rate caps and floors Yes

Warrants (retail options) Yes Yes

Warrants (call options) Yes Yes

Callable and puttable bonds Yes

Convertible bonds Yes

Other

Products of securitisation Yes

Insurance derivatives

Electricity derivatives

Credit derivatives Yes

Weather derivatives

1. On interest rate swaps. 2 = Interest rate swaps. 3 = Equity swaps. 4 = Currency swaps. 5 = Commodity swaps.

192


Questions

1. There is general agreement that securitisation instruments are also derivatives. True or false?

2. A credit derivative may be defined as “… a contract where the payoffs depend partly upon the

creditworthiness of one or more commercial or sovereign entities. True or false?

3. A credit default swap offers a protection purchaser protection against the occurrence of a credit event

during the life of the contract. For this protection the protection purchaser makes a premium payment to

the protection seller on the contract date when the swap is entered into. True or false?

4. The primary objective of weather derivatives is to hedge the risk of the price of a commodity changing

adversely as a result of the weather. True or false?

5. Define seruritisation.

6. The SPV created for the purpose of a securitisation issues 3 streams of MBS in the following manner:

• AAA rated MBS: 90% of the total

• BBB rated MBS: 7% of the total

• Unrated MBS: 3% of the total.

How is each stream generally financed? What does the descriptive name given to each stream indicate

about the risk profile of each stream?

7. The pricing of credit derivatives is determined with the equation:

DSP = RP = ytm – rfr.

What is the meaning of each term in this equation?

8. The relevant information on a credit default swap are:

• The risk free rate – rfr – is 8.9% pa on a synthetic risk-free security.

• The ytm of the reference bond is 12.2% pa.

• The DSP = 3.2% pa.

Will it pay the protection seller to short the reference bond and enter into the swap?

9. What is the underlying instrument for a weather derivative?

10. Why would a company use weather derivatives rather than insurance?

193

Answers

1. False. The products of securitisation may also be seen as “derivatives” because they and their prices are

derived from debt or other securities that are placed in a legal vehicle such as a company or a trust. Some

analysts will insist that these products are not derivatives. However, the jury is still out in this respect.

2. True.

3. False. A credit default swap is a bilateral contract between a protection purchaser and a protection seller

that compensates the purchaser upon the occurrence of a credit event during the life of the contract. For

this protection the protection purchaser makes periodic payments to the protection seller.

4. False. The primary objective of weather derivatives is to hedge volume risks, rather than price risks, that

result from a change in the demand for goods due to a change in weather.

5. Securitisation amounts to the pooling of certain non-marketable assets that have a regular cash flow in a

legal vehicle created for this purpose (called a special purpose vehicle or SPV) and the issuing by the SPV

of marketable securities to finance the pool of assets. The regular cash flow generated by the assets in

the SPV is used to service the interest payable on the securities issued by the SPV.

6. The AAA rated paper is usually sold to the market at a rate commensurate with its risk rating, while the

BBB paper is usually purchased by one of the sponsors at an attractive rate of interest. The management

company usually holds the unrated paper in portfolio, and a mixture of equity and debt finance is used to

finance this company.

The AAA rated paper is referred to as senior debt because it will be paid back before the other two

streams.

The BBB rated paper is referred to as mezzanine debt as it is given an "in-between" position as far as pay

back is concerned. It will be paid back before the unrated paper but only after the AAA paper has been

paid back.

The unrated paper is referred to as subordinated debt as it is last in the queue when it comes to

being paid back.

7. The terms in the credit default swap equation have the following meaning:

• DSP: The fee payable on the swap, i.e. the default swap spread.

• RP: The risk premium.

• ytm: the yield to maturity – the current market return on a reference bond.

• rfr: The risk-free rate – rate on equivalent term government bonds.

194

8. It does not pay the protection seller to short the reference bond and enter into the swap. Doing so means

that the protection seller is borrowing money at 12.2% pa (the ytm at which the reference bond is sold),

and investing at the rfr (8.9% pa) and earning the DSP of 3.2% pa, i.e. a loss of 100 bp.

9. The underlying “instrument” or “value” in the case of temperature-related weather derivatives is Celsius-

scale temperature as measured by “degree days” (DD). A DD is the absolute value of the difference

between the average daily temperature and 18oC. The winter measure of average daily temperature

below 18oC is called heating degree days (HDDs), and the summer measure of average daily temperature

above 18oC is termed cooling degree days (CDDs).

10. Weather derivative products offer weather-sensitive industries a risk management tool that allows them

to efficiently hedge weather risks that were previously uninsurable. Weather derivatives are struck close

to the mean to cover non-catastrophic events and unlike insurance they are contracts of difference, not a

contract of indemnity.

195

CHAPTER 7: GLOSSARY OF TERMS81

11

Arbitrage

Trading strategies designed to profit from price differences for the same or similar goods in different

markets.

Call option

See options.

Clearing

The settlement of a transaction, often involving exchange of payments and/or documentation.

Clearing house

An institution that acts as the buyer to every seller and the seller to every buyer of exchange traded

contracts and thus guarantees the performance of the contract. It is able to incur the enormous credit risks

that this involves as a result of a system of deposits known as margins.

Derivative

Forwards, futures, swaps and options (and other such as weather derivatives) whose value depends, at least

in part, upon the value of an underlying asset or liability.

Equity derivative

A generic term for derivatives involving stocks/shares - whether in terms of those in individual companies, or

baskets or indices of these.

Equity option

An option involving a stock/share, or a basket or index of these.

Exchange traded

The generic term used to describe shares, bonds, futures, options and other derivative instruments traded

on an organised exchange.

Exercise

The act by which the buyer/holder of an option takes up his rights to buy or sell the underlying at the strike

price.

Exercise price

See strike price.

81 From www.safex.co.za with some amendments.

196

Expiry, expiration date, maturity date

The date and time when a transaction matures. Most commonly used to describe when the buyer / holder of

an option ceases to have any rights under the contract, or when a futures contract month ceases trading.

Forward

Any transaction in which the price is fixed today, but settlement is not due to take place until a future date.

Future

An agreement to buy/sell, a standard quantity of a specific commodity or financial instrument, at a standard

future date at a price agreed between parties to the contract. Futures contracts are traded on organised

exchanges.

Greek letters

In the derivative markets reference is made to the Greek letters:

Delta: change in option price per USD (ZAR etc) increase in underlying asset

Gamma: change in delta per USD (ZAR etc) increase in underlying asset

Vega: change in option price per 1% increase in volatility (e.g. from 19% to 20%)

Rho: change in option price per 1% increase in interest rate (e.g. from 4% to 5%)

Theta: change in option price per calendar day passing.82

Hedging

Dealing in such a manner as to reduce risk by taking a position that offsets an existing or anticipated

exposure to a change in market prices. You are therefore attempting to lock in the profit/loss on the position

at the current level.

Initial margin

A relatively small deposit (in comparison to the nominal value of the contract) which both the buyer and the

seller must lodge with the clearing house as security. In very volatile markets, the initial margin required can

vary several times during the course of a single day.

Long position

The result of a trader having bought more than he has sold in any particular

market/commodity/instrument/contract.

82 Adapted from Hull (2000).

197

Margin

Those involved in exchange traded derivatives have to pay margins to the clearing house, either directly, if

they are members, or via their broker. These are posted as a “good-faith” performance guarantee designed

to ensure that all parties are able to fulfill their obligations to one another. Margin accounts are adjusted

daily to reflect current market price on the positions held. If a profit has been made it is paid to the account

holder on a daily basis, likewise, if a loss has been made the account holder is asked to reimburse the

amount lost daily.

Margin call

A demand from the clearing house to one of its members, or a broker (normally a member) to one of its

customers, for a margin payment.

Mark to market

The revaluation of a futures or options position at its current market price/rate. All positions are marked to

market by the clearing house, at least once a day. The profit/loss that is revealed by the re-valuation is

received/paid to the clearing house (known as variation margin).

Maturity

The date when a transaction is due to end, or the period of time until that date is reached.

Open Interest

The total number of purchased or sold lots in a particular type of exchange traded contract that have not yet

been offset, i.e. sold off or bought back.

Option

Contracts which give the buyer/seller the contractual right, but not the obligation, to buy/sell a specified

quantity of a given underlying asset at a fixed price on the designated future date. A call option confers the

buyer/holder the right to buy the underlying commodity/instrument at the strike price. A put option, on the

other hand, confers to the buyer/holder the right to sell the underlying commodity/instrument. The holder

of a long call position will profit from a rise in the price of the underlying asset, while the holder of a long put

position will profit from a fall in the price of the underlying asset.

Over the counter (OTC)

The term “over the counter” is used to describe trading in financial instruments off organised exchanges

with the effect that performance risk by the counterparties is not guaranteed by the exchange

Position

The difference between the quantities bought and sold in any particular market / commodity / instrument /

contract.

Premium

The consideration paid by the buyer/holder to the seller/writer for an option.

198

Put option

See options

Risk management

The science of identifying, assessing, monitoring and controlling risks in order to keep them within

acceptable bounds.

Seat

The right which confers membership of Safex on the registered holder or lessee thereof.

Short position

The result of a trader having sold more than he has bought in any particular market/ commodity /

instrument / contract.

Spot (or cash market)

A transaction involving immediate settlement, or the soonest standard settlement in that market. For

example, the spot date in the foreign exchange market, is normally two business days after the date of the

deal.

Strike price

The price at which the buyer/holder of an option has the right to buy/sell the underlying.

Underlying

The commodity / asset / financial instrument on which a derivative is based. For example, in the case of an

option, the product which the buyer/holder has the right to buy / sell.

Variation margin

See mark to market.

Volatility

A measure of the degree of movements in the price of the underlying around their statistical mean.

Writer

The original seller of an option. The writer is required to fulfill the terms of the option at the choice of the

holder.

199

CHAPTER 8: BIBLIOGRAPHY

Applied Derivatives Trading Magazine, 1998. November.

Bodie, Z, Kane, A, Marcus, AJ, 1999. Investments. Boston: McGraw-Hill/Irwin.

Clemmons, L and Mooney, N, 1999. How weather hedging can keep you cool. The Southern African Treasurer. 11,

December.

Collings, BAC, 1993. The economic impact of an efficient financial futures market on the South African economy.

Unpublished MEcon thesis, University of Stellenbosch, December.

Falkena, HB, et al., 1989. The futures market. Halfway House: Southern Book Publishers (Pty) Limited.

Falkena, HB, et al., 1991. The options market. Halfway House: Southern Book Publishers (Pty) Limited.

Faure, AP, 2005. The financial system. Cape Town: QUOIN Institute (Pty) Limited.

Hull, JC, 2000. Options, futures, & other derivatives (4e). London Prentice-Hall International, Inc.

Lehman Brothers International (Europe), 2001. Credit derivatives explained: markets, products and regulations. March.

McInish, TH, 2000. Capital markets: A global perspective. Massachusetts, USA: Blackwell Publishers Inc.

Mishkin, FS and Eakins, SG, 2000. Financial markets and institutions (3e). Reading, Massachusetts: Addison-Wesley,.

National Treasury, 2001. Separate trading of registered interest and principal of South African government securities.

Draft paper. 2 October.

Rose, PS, 2000. Money and capital markets (international edition). New York: McGraw-Hill Higher Education.

SAFEX (Financial Derivatives and Agricultural Products Divisions of the JSE Securities Exchange South Africa), 2003.

[Online]. Available: www.safex.co.za. [Accessed October].

Saunders, A, 2001. Financial markets and institutions (international edition) New York: McGraw-Hill Higher Education.

Santomero, AM and Babbel, DF, 2001. Financial markets, instruments and institutions (2e). Boston:.McGraw-Hill/Irwin.

Spangenberg, P, 2000. Forward rate agreements. The Southern African Treasurer. 14. September.

Spangenberg, P, 1999. The mechanics of option-styled interest rate derivatives – caps and floors. The Southern African

Treasurer. 11. December.

Standard Bank., 2004. [Online]. Available: www.warrants.co.za. [Accessed June].

Steiner, R, 1998. Mastering financial calculations. London: Financial Times Management.

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